diff --git a/src/mux_h1.c b/src/mux_h1.c
index a00ac60f2..1f8cad245 100644
--- a/src/mux_h1.c
+++ b/src/mux_h1.c
@@ -990,6 +990,8 @@ static int h1_init(struct connection *conn, struct proxy *proxy, struct session
 		tasklet_free(h1c->wait_event.tasklet);
 	pool_free(pool_head_h1c, h1c);
  fail_h1c:
+	if (!conn_is_back(conn))
+		LIST_DEL_INIT(&conn->stopping_list);
 	conn->ctx = conn_ctx; // restore saved context
 	TRACE_DEVEL("leaving in error", H1_EV_H1C_NEW|H1_EV_H1C_END|H1_EV_H1C_ERR);
 	return -1;
diff --git a/src/mux_h2.c b/src/mux_h2.c
index 6338cf02c..ddc19c176 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -1042,6 +1042,8 @@ static int h2_init(struct connection *conn, struct proxy *prx, struct session *s
 		tasklet_free(h2c->wait_event.tasklet);
 	pool_free(pool_head_h2c, h2c);
   fail_no_h2c:
+	if (!conn_is_back(conn))
+		LIST_DEL_INIT(&conn->stopping_list);
 	conn->ctx = conn_ctx; /* restore saved ctx */
 	TRACE_DEVEL("leaving in error", H2_EV_H2C_NEW|H2_EV_H2C_END|H2_EV_H2C_ERR);
 	return -1;