diff --git a/lisp/tramp.el b/lisp/tramp.el
index 24b7c45d..50945ccb 100644
--- a/lisp/tramp.el
+++ b/lisp/tramp.el
@@ -5746,6 +5746,17 @@ Mostly useful to protect BODY from being interrupted by timers."
 This is needed in order to hide `last-coding-system-used', which is set
 for process communication also.
 If the user quits via `C-g', it is propagated up to `tramp-file-name-handler'."
+  ;; There could be other processes which use the same socket for
+  ;; communication.  This could block the output for the current
+  ;; process.  Read such output first.  (Bug#61350)
+  ;; If `timeout' is nil, `accept-process-output' for `proc' could
+  ;; block another such a process.  So we set `timeout' to 0 then.
+  (dolist (p (delq proc (process-list)))
+    (when (tramp-file-name-equal-p
+	   (process-get proc 'vector) (process-get p 'vector))
+      (setq timeout  (or timeout 0))
+      (accept-process-output p 0 nil t)))
+
   (with-current-buffer (process-buffer proc)
     (let ((inhibit-read-only t)
 	  last-coding-system-used