--- ajax_comments/ajax_comments.module	Sat Oct 30 20:00:52 2010
+++ ajax_comments/ajax_comments.module	Sat Oct 30 19:58:34 2010
@@ -253,7 +253,7 @@
   $comment = $variables['comment'];
 
   // Insert proper delete links (fix until hook_link_alter will not work propertly)
-  if ($variables['links'] && user_access('administer comments')) {
+  if ($variables['links'] && user_access('administer comments') || user_access('delete any comment') || user_access('delete any comments at anytime')) {
     $links = module_invoke_all('link', 'comment', $comment, 0);
     $links['comment_delete'] = array(
       'title' => t('delete'),