--- /Users/jacques/Downloads/wordpress/wp-includes/comment-template.php
+++ comment-template2.php
@@ -306,10 +306,10 @@
 	// Get the comment type (comment, trackback),
 	$classes[] = ( empty( $comment->comment_type ) ) ? 'comment' : $comment->comment_type;
 
-	// If the comment author has an id (registered), then print the log in name
+	// If the comment author has an id (registered) for the network, then print the log in name
 	if ( $comment->user_id > 0 && $user = get_userdata($comment->user_id) ) {
 		// For all registered users, 'byuser'
-		$classes[] = 'byuser';
+		$classes[] = 'bynetworkuser';
 		$classes[] = 'comment-author-' . sanitize_html_class($user->user_nicename, $comment->user_id);
 		// For comment authors who are the author of the post
 		if ( $post = get_post($post_id) ) {
@@ -317,6 +317,11 @@
 				$classes[] = 'bypostauthor';
 		}
 	}
+	
+	// If the user belongs to this blog, give them a byuser CSS class
+	if ( is_user_member_of_blog( $comment->user_id, get_current_blog_id() ) ) {
+	  $classes[] = 'byuser';
+	}
 
 	if ( empty($comment_alt) )
 		$comment_alt = 0;