diff --git a/include/haproxy/connection-t.h b/include/haproxy/connection-t.h
index c5d98e7..2f3296d 100644
--- a/include/haproxy/connection-t.h
+++ b/include/haproxy/connection-t.h
@@ -296,6 +296,7 @@
 	MX_FL_CLEAN_ABRT  = 0x00000001, /* abort is clearly reported as an error */
 	MX_FL_HTX         = 0x00000002, /* set if it is an HTX multiplexer */
 	MX_FL_HOL_RISK    = 0x00000004, /* set if the protocol is subject the to head-of-line blocking on server */
+	MX_FL_NO_UPG      = 0x00000008, /* set if mux does not support any upgrade */
 };
 
 /* PROTO token registration */
diff --git a/src/mux_fcgi.c b/src/mux_fcgi.c
index 780d721..ddb2a60 100644
--- a/src/mux_fcgi.c
+++ b/src/mux_fcgi.c
@@ -4240,7 +4240,7 @@
 	.ctl           = fcgi_ctl,
 	.show_fd       = fcgi_show_fd,
 	.takeover      = fcgi_takeover,
-	.flags         = MX_FL_HTX|MX_FL_HOL_RISK,
+	.flags         = MX_FL_HTX|MX_FL_HOL_RISK|MX_FL_NO_UPG,
 	.name          = "FCGI",
 };
 
diff --git a/src/mux_h2.c b/src/mux_h2.c
index 235eb6d..cba19d9 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -6677,7 +6677,7 @@
 	.ctl = h2_ctl,
 	.show_fd = h2_show_fd,
 	.takeover = h2_takeover,
-	.flags = MX_FL_CLEAN_ABRT|MX_FL_HTX|MX_FL_HOL_RISK,
+	.flags = MX_FL_CLEAN_ABRT|MX_FL_HTX|MX_FL_HOL_RISK|MX_FL_NO_UPG,
 	.name = "H2",
 };