diff --git a/include/common/standard.h b/include/common/standard.h
index be85bb5e7..0f4b1870e 100644
--- a/include/common/standard.h
+++ b/include/common/standard.h
@@ -737,6 +737,10 @@ extern time_t my_timegm(const struct tm *tm);
 extern const char *parse_time_err(const char *text, unsigned *ret, unsigned unit_flags);
 extern const char *parse_size_err(const char *text, unsigned *ret);
 
+/* special return values for the time parser */
+#define PARSE_TIME_UNDER ((char *)1)
+#define PARSE_TIME_OVER  ((char *)2)
+
 /* unit flags to pass to parse_time_err */
 #define TIME_UNIT_US   0x0000
 #define TIME_UNIT_MS   0x0001
diff --git a/src/arg.c b/src/arg.c
index b0fe94544..2719b5395 100644
--- a/src/arg.c
+++ b/src/arg.c
@@ -222,8 +222,11 @@ int make_arg_list(const char *in, int len, uint64_t mask, struct arg **argp,
 				goto empty_err;
 
 			ptr_err = parse_time_err(word, &uint, TIME_UNIT_MS);
-			if (ptr_err)
+			if (ptr_err) {
+				if (ptr_err == PARSE_TIME_OVER || ptr_err == PARSE_TIME_UNDER)
+					ptr_err = word;
 				goto parse_err;
+			}
 			arg->data.sint = uint;
 			arg->type = ARGT_SINT;
 			break;
diff --git a/src/cfgparse-global.c b/src/cfgparse-global.c
index 8355a8f1b..4ecaff1ae 100644
--- a/src/cfgparse-global.c
+++ b/src/cfgparse-global.c
@@ -263,9 +263,21 @@ int cfg_parse_global(const char *file, int linenum, char **args, int kwm)
 		}
 
 		res = parse_time_err(args[1], &idle, TIME_UNIT_MS);
-		if (res) {
+		if (res == PARSE_TIME_OVER) {
+			ha_alert("parsing [%s:%d]: timer overflow in argument <%s> to <%s>, maximum value is 65535 ms.\n",
+			         file, linenum, args[1], args[0]);
+			err_code |= ERR_ALERT | ERR_FATAL;
+			goto out;
+		}
+		else if (res == PARSE_TIME_UNDER) {
+			ha_alert("parsing [%s:%d]: timer underflow in argument <%s> to <%s>, minimum non-null value is 1 ms.\n",
+			         file, linenum, args[1], args[0]);
+			err_code |= ERR_ALERT | ERR_FATAL;
+			goto out;
+		}
+		else if (res) {
 			ha_alert("parsing [%s:%d]: unexpected character '%c' in argument to <%s>.\n",
-			      file, linenum, *res, args[0]);
+			         file, linenum, *res, args[0]);
 			err_code |= ERR_ALERT | ERR_FATAL;
 			goto out;
 		}
@@ -942,15 +954,21 @@ int cfg_parse_global(const char *file, int linenum, char **args, int kwm)
 		}
 
 		err = parse_time_err(args[1], &val, TIME_UNIT_MS);
-		if (err) {
+		if (err == PARSE_TIME_OVER) {
+			ha_alert("parsing [%s:%d]: timer overflow in argument <%s> to <%s>, maximum value is 2147483647 ms (~24.8 days).\n",
+			         file, linenum, args[1], args[0]);
+			err_code |= ERR_ALERT | ERR_FATAL;
+		}
+		else if (err == PARSE_TIME_UNDER) {
+			ha_alert("parsing [%s:%d]: timer underflow in argument <%s> to <%s>, minimum non-null value is 1 ms.\n",
+			         file, linenum, args[1], args[0]);
+			err_code |= ERR_ALERT | ERR_FATAL;
+		}
+		else if (err) {
 			ha_alert("parsing [%s:%d]: unsupported character '%c' in '%s' (wants an integer delay).\n", file, linenum, *err, args[0]);
 			err_code |= ERR_ALERT | ERR_FATAL;
 		}
 		global.max_spread_checks = val;
-		if (global.max_spread_checks < 0) {
-			ha_alert("parsing [%s:%d]: '%s' needs a positive delay in milliseconds.\n",file, linenum, args[0]);
-			err_code |= ERR_ALERT | ERR_FATAL;
-		}
 	}
 	else if (strcmp(args[0], "cpu-map") == 0) {
 		/* map a process list to a CPU set */
diff --git a/src/cfgparse-listen.c b/src/cfgparse-listen.c
index 7ffc0e094..d659779a8 100644
--- a/src/cfgparse-listen.c
+++ b/src/cfgparse-listen.c
@@ -1067,7 +1067,19 @@ int cfg_parse_listen(const char *file, int linenum, char **args, int kwm)
 				}
 
 				res = parse_time_err(args[cur_arg + 1], &maxidle, TIME_UNIT_S);
-				if (res) {
+				if (res == PARSE_TIME_OVER) {
+					ha_alert("parsing [%s:%d]: timer overflow in argument <%s> to <%s>, maximum value is 2147483647 s (~68 years).\n",
+						 file, linenum, args[cur_arg+1], args[cur_arg]);
+					err_code |= ERR_ALERT | ERR_FATAL;
+					goto out;
+				}
+				else if (res == PARSE_TIME_UNDER) {
+					ha_alert("parsing [%s:%d]: timer underflow in argument <%s> to <%s>, minimum non-null value is 1 s.\n",
+						 file, linenum, args[cur_arg+1], args[cur_arg]);
+					err_code |= ERR_ALERT | ERR_FATAL;
+					goto out;
+				}
+				else if (res) {
 					ha_alert("parsing [%s:%d]: unexpected character '%c' in argument to <%s>.\n",
 						 file, linenum, *res, args[cur_arg]);
 					err_code |= ERR_ALERT | ERR_FATAL;
@@ -1087,8 +1099,21 @@ int cfg_parse_listen(const char *file, int linenum, char **args, int kwm)
 					goto out;
 				}
 
+
 				res = parse_time_err(args[cur_arg + 1], &maxlife, TIME_UNIT_S);
-				if (res) {
+				if (res == PARSE_TIME_OVER) {
+					ha_alert("parsing [%s:%d]: timer overflow in argument <%s> to <%s>, maximum value is 2147483647 s (~68 years).\n",
+						 file, linenum, args[cur_arg+1], args[cur_arg]);
+					err_code |= ERR_ALERT | ERR_FATAL;
+					goto out;
+				}
+				else if (res == PARSE_TIME_UNDER) {
+					ha_alert("parsing [%s:%d]: timer underflow in argument <%s> to <%s>, minimum non-null value is 1 s.\n",
+						 file, linenum, args[cur_arg+1], args[cur_arg]);
+					err_code |= ERR_ALERT | ERR_FATAL;
+					goto out;
+				}
+				else if (res) {
 					ha_alert("parsing [%s:%d]: unexpected character '%c' in argument to <%s>.\n",
 						 file, linenum, *res, args[cur_arg]);
 					err_code |= ERR_ALERT | ERR_FATAL;
@@ -1932,8 +1957,20 @@ int cfg_parse_listen(const char *file, int linenum, char **args, int kwm)
 			unsigned interval;
 
 			err = parse_time_err(args[2], &interval, TIME_UNIT_S);
-			if (err) {
-				ha_alert("parsing [%s:%d] : unexpected character '%c' in stats refresh interval.\n",
+			if (err == PARSE_TIME_OVER) {
+				ha_alert("parsing [%s:%d]: timer overflow in argument <%s> to stats refresh interval, maximum value is 2147483647 s (~68 years).\n",
+					 file, linenum, args[2]);
+				err_code |= ERR_ALERT | ERR_FATAL;
+				goto out;
+			}
+			else if (err == PARSE_TIME_UNDER) {
+				ha_alert("parsing [%s:%d]: timer underflow in argument <%s> to stats refresh interval, minimum non-null value is 1 s.\n",
+					 file, linenum, args[2]);
+				err_code |= ERR_ALERT | ERR_FATAL;
+				goto out;
+			}
+			else if (err) {
+				ha_alert("parsing [%s:%d]: unexpected character '%c' in argument to stats refresh interval.\n",
 					 file, linenum, *err);
 				err_code |= ERR_ALERT | ERR_FATAL;
 				goto out;
@@ -3374,7 +3411,19 @@ stats_error_parsing:
 			goto out;
 		}
 		err = parse_time_err(args[1], &val, TIME_UNIT_MS);
-		if (err) {
+		if (err == PARSE_TIME_OVER) {
+			ha_alert("parsing [%s:%d]: timer overflow in argument <%s> to grace time, maximum value is 2147483647 ms (~24.8 days).\n",
+			         file, linenum, args[1]);
+			err_code |= ERR_ALERT | ERR_FATAL;
+			goto out;
+		}
+		else if (err == PARSE_TIME_UNDER) {
+			ha_alert("parsing [%s:%d]: timer underflow in argument <%s> to grace time, minimum non-null value is 1 ms.\n",
+			         file, linenum, args[1]);
+			err_code |= ERR_ALERT | ERR_FATAL;
+			goto out;
+		}
+		else if (err) {
 			ha_alert("parsing [%s:%d] : unexpected character '%c' in grace time.\n",
 				 file, linenum, *err);
 			err_code |= ERR_ALERT | ERR_FATAL;
diff --git a/src/cfgparse.c b/src/cfgparse.c
index 98adadffa..1101470be 100644
--- a/src/cfgparse.c
+++ b/src/cfgparse.c
@@ -1203,7 +1203,19 @@ resolv_out:
 			goto out;
 		}
 		res = parse_time_err(args[2], &time, TIME_UNIT_MS);
-		if (res) {
+		if (res == PARSE_TIME_OVER) {
+			ha_alert("parsing [%s:%d]: timer overflow in argument <%s> to <%s>, maximum value is 2147483647 ms (~24.8 days).\n",
+			         file, linenum, args[1], args[0]);
+			err_code |= ERR_ALERT | ERR_FATAL;
+			goto out;
+		}
+		else if (res == PARSE_TIME_UNDER) {
+			ha_alert("parsing [%s:%d]: timer underflow in argument <%s> to <%s>, minimum non-null value is 1 ms.\n",
+			         file, linenum, args[1], args[0]);
+			err_code |= ERR_ALERT | ERR_FATAL;
+			goto out;
+		}
+		else if (res) {
 			ha_alert("parsing [%s:%d]: unexpected character '%c' in argument to <%s>.\n",
 				 file, linenum, *res, args[0]);
 			err_code |= ERR_ALERT | ERR_FATAL;
@@ -1283,7 +1295,19 @@ resolv_out:
 				goto out;
 			}
 			res = parse_time_err(args[2], &tout, TIME_UNIT_MS);
-			if (res) {
+			if (res == PARSE_TIME_OVER) {
+				ha_alert("parsing [%s:%d]: timer overflow in argument <%s> to <%s %s>, maximum value is 2147483647 ms (~24.8 days).\n",
+					 file, linenum, args[2], args[0], args[1]);
+				err_code |= ERR_ALERT | ERR_FATAL;
+				goto out;
+			}
+			else if (res == PARSE_TIME_UNDER) {
+				ha_alert("parsing [%s:%d]: timer underflow in argument <%s> to <%s %s>, minimum non-null value is 1 ms.\n",
+					 file, linenum, args[2], args[0], args[1]);
+				err_code |= ERR_ALERT | ERR_FATAL;
+				goto out;
+			}
+			else if (res) {
 				ha_alert("parsing [%s:%d]: unexpected character '%c' in argument to <%s %s>.\n",
 					 file, linenum, *res, args[0], args[1]);
 				err_code |= ERR_ALERT | ERR_FATAL;
@@ -1459,14 +1483,21 @@ int cfg_parse_mailers(const char *file, int linenum, char **args, int kwm)
 				goto out;
 			}
 			res = parse_time_err(args[2], &timeout_mail, TIME_UNIT_MS);
-			if (res) {
-				ha_alert("parsing [%s:%d]: unexpected character '%c' in argument to <%s>.\n",
-					 file, linenum, *res, args[0]);
+			if (res == PARSE_TIME_OVER) {
+				ha_alert("parsing [%s:%d]: timer overflow in argument <%s> to <%s %s>, maximum value is 2147483647 ms (~24.8 days).\n",
+					 file, linenum, args[2], args[0], args[1]);
 				err_code |= ERR_ALERT | ERR_FATAL;
 				goto out;
 			}
-			if (timeout_mail <= 0) {
-				ha_alert("parsing [%s:%d] : '%s %s' expects a positive <time> argument.\n", file, linenum, args[0], args[1]);
+			else if (res == PARSE_TIME_UNDER) {
+				ha_alert("parsing [%s:%d]: timer underflow in argument <%s> to <%s %s>, minimum non-null value is 1 ms.\n",
+					 file, linenum, args[2], args[0], args[1]);
+				err_code |= ERR_ALERT | ERR_FATAL;
+				goto out;
+			}
+			else if (res) {
+				ha_alert("parsing [%s:%d]: unexpected character '%c' in argument to <%s %s>.\n",
+					 file, linenum, *res, args[0], args[1]);
 				err_code |= ERR_ALERT | ERR_FATAL;
 				goto out;
 			}
diff --git a/src/cli.c b/src/cli.c
index 9949a885a..25743d92c 100644
--- a/src/cli.c
+++ b/src/cli.c
@@ -309,7 +309,17 @@ static int stats_parse_global(char **args, int section_type, struct proxy *curpx
 		unsigned timeout;
 		const char *res = parse_time_err(args[2], &timeout, TIME_UNIT_MS);
 
-		if (res) {
+		if (res == PARSE_TIME_OVER) {
+			memprintf(err, "timer overflow in argument '%s' to '%s %s' (maximum value is 2147483647 ms or ~24.8 days)",
+				 args[2], args[0], args[1]);
+			return -1;
+		}
+		else if (res == PARSE_TIME_UNDER) {
+			memprintf(err, "timer underflow in argument '%s' to '%s %s' (minimum non-null value is 1 ms)",
+				 args[2], args[0], args[1]);
+			return -1;
+		}
+		else if (res) {
 			memprintf(err, "'%s %s' : unexpected character '%c'", args[0], args[1], *res);
 			return -1;
 		}
diff --git a/src/flt_spoe.c b/src/flt_spoe.c
index 711ac809e..f20b2640b 100644
--- a/src/flt_spoe.c
+++ b/src/flt_spoe.c
@@ -3482,7 +3482,19 @@ cfg_parse_spoe_agent(const char *file, int linenum, char **args, int kwm)
 			goto out;
 		}
 		res = parse_time_err(args[2], &timeout, TIME_UNIT_MS);
-		if (res) {
+		if (res == PARSE_TIME_OVER) {
+			ha_alert("parsing [%s:%d]: timer overflow in argument <%s> to <%s %s>, maximum value is 2147483647 ms (~24.8 days).\n",
+				 file, linenum, args[2], args[0], args[1]);
+			err_code |= ERR_ALERT | ERR_FATAL;
+			goto out;
+		}
+		else if (res == PARSE_TIME_UNDER) {
+			ha_alert("parsing [%s:%d]: timer underflow in argument <%s> to <%s %s>, minimum non-null value is 1 ms.\n",
+				 file, linenum, args[2], args[0], args[1]);
+			err_code |= ERR_ALERT | ERR_FATAL;
+			goto out;
+		}
+		else if (res) {
 			ha_alert("parsing [%s:%d] : unexpected character '%c' in 'timeout %s'.\n",
 				 file, linenum, *res, args[1]);
 			err_code |= ERR_ALERT | ERR_FATAL;
diff --git a/src/hlua.c b/src/hlua.c
index ef796327d..28abd0836 100644
--- a/src/hlua.c
+++ b/src/hlua.c
@@ -8073,7 +8073,17 @@ static int hlua_read_timeout(char **args, int section_type, struct proxy *curpx,
 	const char *error;
 
 	error = parse_time_err(args[1], timeout, TIME_UNIT_MS);
-	if (error && *error != '\0') {
+	if (error == PARSE_TIME_OVER) {
+		memprintf(err, "timer overflow in argument <%s> to <%s> (maximum value is 2147483647 ms or ~24.8 days)",
+			  args[1], args[0]);
+		return -1;
+	}
+	else if (error == PARSE_TIME_UNDER) {
+		memprintf(err, "timer underflow in argument <%s> to <%s> (minimum non-null value is 1 ms)",
+			  args[1], args[0]);
+		return -1;
+	}
+	else if (error) {
 		memprintf(err, "%s: invalid timeout", args[0]);
 		return -1;
 	}
diff --git a/src/proto_tcp.c b/src/proto_tcp.c
index 51d10a553..64ffb83c5 100644
--- a/src/proto_tcp.c
+++ b/src/proto_tcp.c
@@ -1816,7 +1816,17 @@ static int bind_parse_tcp_ut(char **args, int cur_arg, struct proxy *px, struct
 	}
 
 	ptr = parse_time_err(args[cur_arg + 1], &timeout, TIME_UNIT_MS);
-	if (ptr) {
+	if (ptr == PARSE_TIME_OVER) {
+		memprintf(err, "timer overflow in argument '%s' to '%s' (maximum value is 2147483647 ms or ~24.8 days)",
+			  args[cur_arg+1], args[cur_arg]);
+		return ERR_ALERT | ERR_FATAL;
+	}
+	else if (ptr == PARSE_TIME_UNDER) {
+		memprintf(err, "timer underflow in argument '%s' to '%s' (minimum non-null value is 1 ms)",
+			  args[cur_arg+1], args[cur_arg]);
+		return ERR_ALERT | ERR_FATAL;
+	}
+	else if (ptr) {
 		memprintf(err, "'%s' : expects a positive delay in milliseconds", args[cur_arg]);
 		return ERR_ALERT | ERR_FATAL;
 	}
@@ -1891,7 +1901,17 @@ static int srv_parse_tcp_ut(char **args, int *cur_arg, struct proxy *px, struct
 	}
 
 	ptr = parse_time_err(args[*cur_arg + 1], &timeout, TIME_UNIT_MS);
-	if (ptr) {
+	if (ptr == PARSE_TIME_OVER) {
+		memprintf(err, "timer overflow in argument '%s' to '%s' (maximum value is 2147483647 ms or ~24.8 days)",
+			  args[*cur_arg+1], args[*cur_arg]);
+		return ERR_ALERT | ERR_FATAL;
+	}
+	else if (ptr == PARSE_TIME_UNDER) {
+		memprintf(err, "timer underflow in argument '%s' to '%s' (minimum non-null value is 1 ms)",
+			  args[*cur_arg+1], args[*cur_arg]);
+		return ERR_ALERT | ERR_FATAL;
+	}
+	else if (ptr) {
 		memprintf(err, "'%s' : expects a positive delay in milliseconds", args[*cur_arg]);
 		return ERR_ALERT | ERR_FATAL;
 	}
diff --git a/src/proxy.c b/src/proxy.c
index 575a8eff6..78babd5bb 100644
--- a/src/proxy.c
+++ b/src/proxy.c
@@ -275,7 +275,17 @@ static int proxy_parse_timeout(char **args, int section, struct proxy *proxy,
 	}
 
 	res = parse_time_err(args[1], &timeout, TIME_UNIT_MS);
-	if (res) {
+	if (res == PARSE_TIME_OVER) {
+		memprintf(err, "timer overflow in argument '%s' to 'timeout %s' (maximum value is 2147483647 ms or ~24.8 days)",
+			  args[1], name);
+		return -1;
+	}
+	else if (res == PARSE_TIME_UNDER) {
+		memprintf(err, "timer underflow in argument '%s' to 'timeout %s' (minimum non-null value is 1 ms)",
+			  args[1], name);
+		return -1;
+	}
+	else if (res) {
 		memprintf(err, "unexpected character '%c' in 'timeout %s'", *res, name);
 		return -1;
 	}
@@ -1056,7 +1066,17 @@ static int proxy_parse_hard_stop_after(char **args, int section_type, struct pro
 		return -1;
 	}
 	res = parse_time_err(args[1], &global.hard_stop_after, TIME_UNIT_MS);
-	if (res) {
+	if (res == PARSE_TIME_OVER) {
+		memprintf(err, "timer overflow in argument '%s' to '%s' (maximum value is 2147483647 ms or ~24.8 days)",
+			  args[1], args[0]);
+		return -1;
+	}
+	else if (res == PARSE_TIME_UNDER) {
+		memprintf(err, "timer underflow in argument '%s' to '%s' (minimum non-null value is 1 ms)",
+			  args[1], args[0]);
+		return -1;
+	}
+	else if (res) {
 		memprintf(err, "unexpected character '%c' in argument to <%s>.\n", *res, args[0]);
 		return -1;
 	}
diff --git a/src/server.c b/src/server.c
index 14e1a938c..0cbba7866 100644
--- a/src/server.c
+++ b/src/server.c
@@ -404,7 +404,17 @@ static int srv_parse_pool_purge_delay(char **args, int *cur_arg, struct proxy *c
 		return ERR_ALERT | ERR_FATAL;
 	}
 	res = parse_time_err(arg, &time, TIME_UNIT_MS);
-	if (res) {
+	if (res == PARSE_TIME_OVER) {
+		memprintf(err, "timer overflow in argument '%s' to '%s' (maximum value is 2147483647 ms or ~24.8 days)",
+			  args[*cur_arg+1], args[*cur_arg]);
+		return ERR_ALERT | ERR_FATAL;
+	}
+	else if (res == PARSE_TIME_UNDER) {
+		memprintf(err, "timer underflow in argument '%s' to '%s' (minimum non-null value is 1 ms)",
+			  args[*cur_arg+1], args[*cur_arg]);
+		return ERR_ALERT | ERR_FATAL;
+	}
+	else if (res) {
 		memprintf(err, "unexpected character '%c' in argument to <%s>.\n",
 		    *res, args[*cur_arg]);
 		return ERR_ALERT | ERR_FATAL;
@@ -2305,7 +2315,20 @@ int parse_server(const char *file, int linenum, char **args, struct proxy *curpr
 		while (*args[cur_arg]) {
 			if (!strcmp(args[cur_arg], "agent-inter")) {
 				const char *err = parse_time_err(args[cur_arg + 1], &val, TIME_UNIT_MS);
-				if (err) {
+
+				if (err == PARSE_TIME_OVER) {
+					ha_alert("parsing [%s:%d]: timer overflow in argument <%s> to <%s> of server %s, maximum value is 2147483647 ms (~24.8 days).\n",
+						 file, linenum, args[cur_arg+1], args[cur_arg], newsrv->id);
+					err_code |= ERR_ALERT | ERR_FATAL;
+					goto out;
+				}
+				else if (err == PARSE_TIME_UNDER) {
+					ha_alert("parsing [%s:%d]: timer underflow in argument <%s> to <%s> of server %s, minimum non-null value is 1 ms.\n",
+						 file, linenum, args[cur_arg+1], args[cur_arg], newsrv->id);
+					err_code |= ERR_ALERT | ERR_FATAL;
+					goto out;
+				}
+				else if (err) {
 					ha_alert("parsing [%s:%d] : unexpected character '%c' in 'agent-inter' argument of server %s.\n",
 					      file, linenum, *err, newsrv->id);
 					err_code |= ERR_ALERT | ERR_FATAL;
@@ -2530,7 +2553,20 @@ int parse_server(const char *file, int linenum, char **args, struct proxy *curpr
 			}
 			else if (!strcmp(args[cur_arg], "inter")) {
 				const char *err = parse_time_err(args[cur_arg + 1], &val, TIME_UNIT_MS);
-				if (err) {
+
+				if (err == PARSE_TIME_OVER) {
+					ha_alert("parsing [%s:%d]: timer overflow in argument <%s> to <%s> of server %s, maximum value is 2147483647 ms (~24.8 days).\n",
+						 file, linenum, args[cur_arg+1], args[cur_arg], newsrv->id);
+					err_code |= ERR_ALERT | ERR_FATAL;
+					goto out;
+				}
+				else if (err == PARSE_TIME_UNDER) {
+					ha_alert("parsing [%s:%d]: timer underflow in argument <%s> to <%s> of server %s, minimum non-null value is 1 ms.\n",
+						 file, linenum, args[cur_arg+1], args[cur_arg], newsrv->id);
+					err_code |= ERR_ALERT | ERR_FATAL;
+					goto out;
+				}
+				else if (err) {
 					ha_alert("parsing [%s:%d] : unexpected character '%c' in 'inter' argument of server %s.\n",
 					      file, linenum, *err, newsrv->id);
 					err_code |= ERR_ALERT | ERR_FATAL;
@@ -2547,7 +2583,20 @@ int parse_server(const char *file, int linenum, char **args, struct proxy *curpr
 			}
 			else if (!strcmp(args[cur_arg], "fastinter")) {
 				const char *err = parse_time_err(args[cur_arg + 1], &val, TIME_UNIT_MS);
-				if (err) {
+
+				if (err == PARSE_TIME_OVER) {
+					ha_alert("parsing [%s:%d]: timer overflow in argument <%s> to <%s> of server %s, maximum value is 2147483647 ms (~24.8 days).\n",
+						 file, linenum, args[cur_arg+1], args[cur_arg], newsrv->id);
+					err_code |= ERR_ALERT | ERR_FATAL;
+					goto out;
+				}
+				else if (err == PARSE_TIME_UNDER) {
+					ha_alert("parsing [%s:%d]: timer underflow in argument <%s> to <%s> of server %s, minimum non-null value is 1 ms.\n",
+						 file, linenum, args[cur_arg+1], args[cur_arg], newsrv->id);
+					err_code |= ERR_ALERT | ERR_FATAL;
+					goto out;
+				}
+				else if (err) {
 					ha_alert("parsing [%s:%d]: unexpected character '%c' in 'fastinter' argument of server %s.\n",
 					      file, linenum, *err, newsrv->id);
 					err_code |= ERR_ALERT | ERR_FATAL;
@@ -2564,7 +2613,20 @@ int parse_server(const char *file, int linenum, char **args, struct proxy *curpr
 			}
 			else if (!strcmp(args[cur_arg], "downinter")) {
 				const char *err = parse_time_err(args[cur_arg + 1], &val, TIME_UNIT_MS);
-				if (err) {
+
+				if (err == PARSE_TIME_OVER) {
+					ha_alert("parsing [%s:%d]: timer overflow in argument <%s> to <%s> of server %s, maximum value is 2147483647 ms (~24.8 days).\n",
+						 file, linenum, args[cur_arg+1], args[cur_arg], newsrv->id);
+					err_code |= ERR_ALERT | ERR_FATAL;
+					goto out;
+				}
+				else if (err == PARSE_TIME_UNDER) {
+					ha_alert("parsing [%s:%d]: timer underflow in argument <%s> to <%s> of server %s, minimum non-null value is 1 ms.\n",
+						 file, linenum, args[cur_arg+1], args[cur_arg], newsrv->id);
+					err_code |= ERR_ALERT | ERR_FATAL;
+					goto out;
+				}
+				else if (err) {
 					ha_alert("parsing [%s:%d]: unexpected character '%c' in 'downinter' argument of server %s.\n",
 					      file, linenum, *err, newsrv->id);
 					err_code |= ERR_ALERT | ERR_FATAL;
@@ -2611,7 +2673,20 @@ int parse_server(const char *file, int linenum, char **args, struct proxy *curpr
 			else if (!strcmp(args[cur_arg], "slowstart")) {
 				/* slowstart is stored in seconds */
 				const char *err = parse_time_err(args[cur_arg + 1], &val, TIME_UNIT_MS);
-				if (err) {
+
+				if (err == PARSE_TIME_OVER) {
+					ha_alert("parsing [%s:%d]: timer overflow in argument <%s> to <%s> of server %s, maximum value is 2147483647 ms (~24.8 days).\n",
+						 file, linenum, args[cur_arg+1], args[cur_arg], newsrv->id);
+					err_code |= ERR_ALERT | ERR_FATAL;
+					goto out;
+				}
+				else if (err == PARSE_TIME_UNDER) {
+					ha_alert("parsing [%s:%d]: timer underflow in argument <%s> to <%s> of server %s, minimum non-null value is 1 ms.\n",
+						 file, linenum, args[cur_arg+1], args[cur_arg], newsrv->id);
+					err_code |= ERR_ALERT | ERR_FATAL;
+					goto out;
+				}
+				else if (err) {
 					ha_alert("parsing [%s:%d] : unexpected character '%c' in 'slowstart' argument of server %s.\n",
 					      file, linenum, *err, newsrv->id);
 					err_code |= ERR_ALERT | ERR_FATAL;
diff --git a/src/ssl_sock.c b/src/ssl_sock.c
index 5cc005b7c..b6364faa7 100644
--- a/src/ssl_sock.c
+++ b/src/ssl_sock.c
@@ -9065,7 +9065,17 @@ static int ssl_parse_global_lifetime(char **args, int section_type, struct proxy
 	}
 
 	res = parse_time_err(args[1], &global_ssl.life_time, TIME_UNIT_S);
-	if (res) {
+	if (res == PARSE_TIME_OVER) {
+		memprintf(err, "timer overflow in argument '%s' to <%s> (maximum value is 2147483647 s or ~68 years).",
+			  args[1], args[0]);
+		return -1;
+	}
+	else if (res == PARSE_TIME_UNDER) {
+		memprintf(err, "timer underflow in argument '%s' to <%s> (minimum non-null value is 1 s).",
+			  args[1], args[0]);
+		return -1;
+	}
+	else if (res) {
 		memprintf(err, "unexpected character '%c' in argument to <%s>.", *res, args[0]);
 		return -1;
 	}
diff --git a/src/standard.c b/src/standard.c
index a67948ba5..3651f5e35 100644
--- a/src/standard.c
+++ b/src/standard.c
@@ -2032,12 +2032,15 @@ int strl2llrc_dotted(const char *text, int len, long long *ret)
  * The value is returned in <ret> if everything is fine, and a NULL is returned
  * by the function. In case of error, a pointer to the error is returned and
  * <ret> is left untouched. Values are automatically rounded up when needed.
+ * Values resulting in values larger than or equal to 2^31 after conversion are
+ * reported as an overflow as value PARSE_TIME_OVER. Non-null values resulting
+ * in an underflow are reported as an underflow as value PARSE_TIME_UNDER.
  */
 const char *parse_time_err(const char *text, unsigned *ret, unsigned unit_flags)
 {
-	unsigned imult, idiv;
-	unsigned omult, odiv;
-	unsigned value;
+	unsigned long long imult, idiv;
+	unsigned long long omult, odiv;
+	unsigned long long value, result;
 
 	omult = odiv = 1;
 
@@ -2100,8 +2103,12 @@ const char *parse_time_err(const char *text, unsigned *ret, unsigned unit_flags)
 	if (imult % odiv == 0) { imult /= odiv; odiv = 1; }
 	if (odiv % imult == 0) { odiv /= imult; imult = 1; }
 
-	value = (value * (imult * omult) + (idiv * odiv - 1)) / (idiv * odiv);
-	*ret = value;
+	result = (value * (imult * omult) + (idiv * odiv - 1)) / (idiv * odiv);
+	if (result >= 0x80000000)
+		return PARSE_TIME_OVER;
+	if (!result && value)
+		return PARSE_TIME_UNDER;
+	*ret = result;
 	return NULL;
 }
 
diff --git a/src/stick_table.c b/src/stick_table.c
index a555e6463..4b04f18cc 100644
--- a/src/stick_table.c
+++ b/src/stick_table.c
@@ -769,15 +769,21 @@ int parse_stick_table(const char *file, int linenum, char **args,
 				goto out;
 			}
 			err = parse_time_err(args[idx], &val, TIME_UNIT_MS);
-			if (err) {
-				ha_alert("parsing [%s:%d] : %s: unexpected character '%c' in argument of '%s'.\n",
-					 file, linenum, args[0], *err, args[idx-1]);
+			if (err == PARSE_TIME_OVER) {
+				ha_alert("parsing [%s:%d]: %s: timer overflow in argument <%s> to <%s>, maximum value is 2147483647 ms (~24.8 days).\n",
+					 file, linenum, args[0], args[idx], args[idx-1]);
 				err_code |= ERR_ALERT | ERR_FATAL;
 				goto out;
 			}
-			if (val > INT_MAX) {
-				ha_alert("parsing [%s:%d] : Expire value [%u]ms exceeds maxmimum value of 24.85 days.\n",
-					 file, linenum, val);
+			else if (err == PARSE_TIME_UNDER) {
+				ha_alert("parsing [%s:%d]: %s: timer underflow in argument <%s> to <%s>, minimum non-null value is 1 ms.\n",
+					 file, linenum, args[0], args[idx], args[idx-1]);
+				err_code |= ERR_ALERT | ERR_FATAL;
+				goto out;
+			}
+			else if (err) {
+				ha_alert("parsing [%s:%d] : %s: unexpected character '%c' in argument of '%s'.\n",
+					 file, linenum, args[0], *err, args[idx-1]);
 				err_code |= ERR_ALERT | ERR_FATAL;
 				goto out;
 			}
diff --git a/src/tcp_rules.c b/src/tcp_rules.c
index a70c4c076..72b11ae36 100644
--- a/src/tcp_rules.c
+++ b/src/tcp_rules.c
@@ -922,7 +922,12 @@ static int tcp_parse_tcp_rep(char **args, int section_type, struct proxy *curpx,
 			memprintf(err,
 			          "'%s %s' expects a positive delay in milliseconds, in %s '%s'",
 			          args[0], args[1], proxy_type_str(curpx), curpx->id);
-			if (ptr)
+
+			if (ptr == PARSE_TIME_OVER)
+				memprintf(err, "%s (timer overflow in '%s', maximum value is 2147483647 ms or ~24.8 days)", *err, args[2]);
+			else if (ptr == PARSE_TIME_UNDER)
+				memprintf(err, "%s (timer underflow in '%s', minimum non-null value is 1 ms)", *err, args[2]);
+			else if (ptr)
 				memprintf(err, "%s (unexpected character '%c')", *err, *ptr);
 			return -1;
 		}
@@ -1031,7 +1036,12 @@ static int tcp_parse_tcp_req(char **args, int section_type, struct proxy *curpx,
 			memprintf(err,
 			          "'%s %s' expects a positive delay in milliseconds, in %s '%s'",
 			          args[0], args[1], proxy_type_str(curpx), curpx->id);
-			if (ptr)
+
+			if (ptr == PARSE_TIME_OVER)
+				memprintf(err, "%s (timer overflow in '%s', maximum value is 2147483647 ms or ~24.8 days)", *err, args[2]);
+			else if (ptr == PARSE_TIME_UNDER)
+				memprintf(err, "%s (timer underflow in '%s', minimum non-null value is 1 ms)", *err, args[2]);
+			else if (ptr)
 				memprintf(err, "%s (unexpected character '%c')", *err, *ptr);
 			return -1;
 		}