diff --git a/lisp/files.el b/lisp/files.el
index a6fe381..0d0d6e2 100644
--- a/lisp/files.el
+++ b/lisp/files.el
@@ -5940,8 +5940,8 @@ make-auto-save-file-name
 	    ;; Make sure auto-save file names don't contain characters
 	    ;; invalid for the underlying filesystem.
 	    (if (and (memq system-type '(ms-dos windows-nt cygwin))
-		     ;; Don't modify remote (ange-ftp) filenames
-		     (not (string-match "^/address@hidden:" result)))
+		     ;; Don't modify remote filenames.
+                     (not (file-remote-p result)))
 		(convert-standard-filename result)
 	      result))))
 
@@ -5978,8 +5978,8 @@ make-auto-save-file-name
 		      ((file-writable-p "/var/tmp/") "/var/tmp/")
 		      ("~/")))))
 	       (if (and (memq system-type '(ms-dos windows-nt cygwin))
-			;; Don't modify remote (ange-ftp) filenames
-			(not (string-match "^/address@hidden:" fname)))
+			;; Don't modify remote filenames.
+			(not (file-remote-p fname)))
 		   ;; The call to convert-standard-filename is in case
 		   ;; buffer-name includes characters not allowed by the
 		   ;; DOS/Windows filesystems.  make-temp-file writes to the
diff --git a/lisp/net/tramp.el b/lisp/net/tramp.el
index b4242c0..f350f2a 100644
--- a/lisp/net/tramp.el
+++ b/lisp/net/tramp.el
@@ -4102,7 +4102,11 @@ tramp-handle-make-auto-save-file-name
 	      (file-exists-p tramp-auto-save-directory))
     (make-directory tramp-auto-save-directory t))
 
-  (let ((system-type 'not-windows)
+  (let ((system-type
+	 (if (and (stringp tramp-auto-save-directory)
+		  (file-remote-p tramp-auto-save-directory))
+	     'not-windows
+	   system-type))
 	(auto-save-file-name-transforms
 	 (if (and (null tramp-auto-save-directory)
 		  (boundp 'auto-save-file-name-transforms))
diff --git a/test/automated/tramp-tests.el b/test/automated/tramp-tests.el
index 83a780d..2c59591 100644
--- a/test/automated/tramp-tests.el
+++ b/test/automated/tramp-tests.el
@@ -1775,13 +1775,17 @@ tramp-test--shell-command-to-string-asynchronously
 	      (should
 	       (string-equal
 		(make-auto-save-file-name)
-		;; This is taken from original `make-auto-save-file-name'.
-		(expand-file-name
-		 (format
-		  "#%s#"
-		  (subst-char-in-string
-		   ?/ ?! (replace-regexp-in-string "!" "!!" tmp-name1)))
-		 temporary-file-directory)))))
+                ;; This is taken from original `make-auto-save-file-name'.
+                ;; We call `convert-standard-filename', because on
+                ;; MS Windows the (local) colons must be replaced by
+                ;; exclamation marks.
+                (convert-standard-filename
+                 (expand-file-name
+                  (format
+                   "#%s#"
+                   (subst-char-in-string
+                    ?/ ?! (replace-regexp-in-string "!" "!!" tmp-name1)))
+                  temporary-file-directory))))))
 
 	  ;; No mapping.
 	  (let (tramp-auto-save-directory auto-save-file-name-transforms)