hook_menu_local_tasks_alter for specific tab
You can use hook_menu_local_tasks_alter() in your template.php file for your theme or .module file in module like below:

function YOURTHEME_menu_local_tasks_alter(&amp;$data, $router_item, $root_path) {

  foreach ($data['tabs'] as $key1 =&gt; $tabs) {
    foreach ($tabs['output'] as $key2 =&gt; $item) {

      if ($item['#link']['path'] == 'node/%/edit' || $item['#link']['path'] == 'user/%/edit') {
        $data['tabs'][$key1]['output'][$key2]['#link']['localized_options']['attributes']['class'][]  = 'CLASS_NAME_HERE';
      }
      else if ($item['#link']['path'] == 'node/%/delete') {
        $data['tabs'][$key1]['output'][$key2]['#link']['localized_options']['attributes']['class'][]  = 'CLASS_NAME_HERE';

      }
      else if ($data['tabs'][$key1]['output'][$key2]['#link']['title'] == 'View') {
        $data['tabs'][$key1]['output'][$key2]['#link']['localized_options']['attributes']['class'][]  = 'CLASS_NAME_HERE'; 

      }
      else if ($item['#link']['path'] == 'node/%/revisions') {
        $data['tabs'][$key1]['output'][$key2]['#link']['localized_options']['attributes']['class'][]  = 'CLASS_NAME_HERE';

      }

    }
  }
}


Hope this will help.