diff --git a/lisp/net/tramp-adb.el b/lisp/net/tramp-adb.el
index dbd13183a92..32fd1888d36 100644
--- a/lisp/net/tramp-adb.el
+++ b/lisp/net/tramp-adb.el
@@ -1250,7 +1250,10 @@ connection if a previous connection has died for some reason."
 		;; Read the expression.
 		(goto-char (point-min))
 		(read (current-buffer)))
-	      ":" 'omit-nulls))))))))
+	      ":" 'omit-nulls))
+
+	    ;; Mark it as connected.
+	    (tramp-set-connection-property p "connected" t)))))))
 
 (add-hook 'tramp-unload-hook
 	  (lambda ()
diff --git a/lisp/net/tramp-gvfs.el b/lisp/net/tramp-gvfs.el
index e19ceae89da..dee8333e547 100644
--- a/lisp/net/tramp-gvfs.el
+++ b/lisp/net/tramp-gvfs.el
@@ -1617,7 +1617,11 @@ connection if a previous connection has died for some reason."
 	;; is marked with the fuse-mountpoint "/".  We shall react.
 	(when (string-equal
 	       (tramp-get-file-property vec "/" "fuse-mountpoint" "") "/")
-	  (tramp-error vec 'file-error "FUSE mount denied")))))
+	  (tramp-error vec 'file-error "FUSE mount denied"))
+
+	;; Mark it as connected.
+	(tramp-set-connection-property
+	 (tramp-get-connection-process vec) "connected" t))))
 
   ;; In `tramp-check-cached-permissions', the connection properties
   ;; {uig,gid}-{integer,string} are used.  We set them to their local
diff --git a/lisp/net/tramp-sh.el b/lisp/net/tramp-sh.el
index 7ace8864f88..1f43747c094 100644
--- a/lisp/net/tramp-sh.el
+++ b/lisp/net/tramp-sh.el
@@ -5040,7 +5040,10 @@ connection if a previous connection has died for some reason."
 			target-alist (cdr target-alist)))
 
 		;; Make initial shell settings.
-		(tramp-open-connection-setup-interactive-shell p vec)))))
+		(tramp-open-connection-setup-interactive-shell p vec)
+
+		;; Mark it as connected.
+		(tramp-set-connection-property p "connected" t)))))
 
       ;; When the user did interrupt, we must cleanup.
       (quit
diff --git a/lisp/net/tramp-smb.el b/lisp/net/tramp-smb.el
index e957fdfd612..509e2e388b8 100644
--- a/lisp/net/tramp-smb.el
+++ b/lisp/net/tramp-smb.el
@@ -1914,7 +1914,10 @@ If ARGUMENT is non-nil, use it as argument for
 		    ;; character by character; if we send the string
 		    ;; at once, it is read painfully slow.
 		    (tramp-set-connection-property p "smb-share" share)
-		    (tramp-set-connection-property p "chunksize" 1))
+		    (tramp-set-connection-property p "chunksize" 1)
+
+		    ;; Mark it as connected.
+		    (tramp-set-connection-property p "connected" t))
 
 		;; Check for the error reason.  If it was due to wrong
 		;; password, reestablish the connection.  We cannot
diff --git a/lisp/net/tramp.el b/lisp/net/tramp.el
index e8e40ae23dc..43962169d5a 100644
--- a/lisp/net/tramp.el
+++ b/lisp/net/tramp.el
@@ -3009,7 +3009,8 @@ User is always nil."
     (when (tramp-tramp-file-p filename)
       (let* ((v (tramp-dissect-file-name filename))
 	     (p (tramp-get-connection-process v))
-	     (c (and p (processp p) (memq (process-status p) '(run open)))))
+	     (c (and p (processp p) (memq (process-status p) '(run open))
+		     (tramp-get-connection-property p "connected" nil))))
 	;; We expand the file name only, if there is already a connection.
 	(with-parsed-tramp-file-name
 	    (if c (expand-file-name filename) filename) nil