diff --git a/lisp/ox-ascii.el b/lisp/ox-ascii.el
index 6fcde013b..3c39225a3 100644
--- a/lisp/ox-ascii.el
+++ b/lisp/ox-ascii.el
@@ -951,12 +951,17 @@ channel."
 	 (when description
 	   (let ((dest (if (equal type "fuzzy")
 			   (org-export-resolve-fuzzy-link link info)
-			 (org-export-resolve-id-link link info))))
-	     (concat
-	      (org-ascii--fill-string
-	       (format "[%s] %s" anchor (org-ascii--describe-datum dest info))
-	       width info)
-	      "\n\n"))))
+                         ;; Ignore broken links.  On broken link,
+                         ;; `org-export-resolve-id-link' will throw an
+                         ;; error and `ignore-error' will return nil.
+			 (ignore-error 'org-link-broken
+                           (org-export-resolve-id-link link info)))))
+             (when dest
+	       (concat
+	        (org-ascii--fill-string
+	         (format "[%s] %s" anchor (org-ascii--describe-datum dest info))
+	         width info)
+	        "\n\n")))))
 	;; Do not add a link that cannot be resolved and doesn't have
 	;; any description: destination is already visible in the
 	;; paragraph.
diff --git a/lisp/ox-md.el b/lisp/ox-md.el
index 127c70cbc..c268aa5dd 100644
--- a/lisp/ox-md.el
+++ b/lisp/ox-md.el
@@ -193,11 +193,10 @@ of contents can refer to headlines."
      ;; A link refers internally to HEADLINE.
      (org-element-map (plist-get info :parse-tree) 'link
        (lambda (link)
-	 (eq headline
-	     (pcase (org-element-property :type link)
-	       ((or "custom-id" "id") (org-export-resolve-id-link link info))
-	       ("fuzzy" (org-export-resolve-fuzzy-link link info))
-	       (_ nil))))
+	 (equal headline
+                ;; Ignore broken links.
+                (ignore-error 'org-link-broken
+                  (org-export-resolve-link link info))))
        info t))))
 
 (defun org-md--headline-title (style level title &optional anchor tags)
diff --git a/lisp/ox.el b/lisp/ox.el
index 8420db7fc..03af47001 100644
--- a/lisp/ox.el
+++ b/lisp/ox.el
@@ -1912,8 +1912,10 @@ Return a string."
 			   (org-element-property :archivedp data)))
 		  (let ((transcoder (org-export-transcoder data info)))
 		    (or (and (functionp transcoder)
-			     (broken-link-handler
-			      (funcall transcoder data nil info)))
+                             (if (eq type 'link)
+			         (broken-link-handler
+			          (funcall transcoder data nil info))
+                               (funcall transcoder data nil info)))
 			;; Export snippets never return a nil value so
 			;; that white spaces following them are never
 			;; ignored.