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Try this, http://api.drupal.org/api/drupal/includes--theme.inc/function/theme_links/7:

function THEMENAME_links__system_MENUNAME_menu($variables) {
  $output = '';
  foreach ($variables['links'] as $link) {
    $output .= l(<li' . drupal_attributes(array('class' => $class)) . '>' .'<span>'. check_plain($link['title']) .'</span>' . '</li>', $link['href'], $link);
  }
  return $output;
}

Is the <li> inside the <a>?

Try this, http://api.drupal.org/api/drupal/includes--theme.inc/function/theme_links/7:

function THEMENAME_links__system_MENUNAME_menu($variables) {
  $output = '';
  foreach ($variables['links'] as $link) {
    $output .= l('<li' . drupal_attributes(array('class' => $class)) . '>' .'<span>'. check_plain($link['title']) .'</span>' . '</li>', $link['href'], $link);
  }
  return $output;
}

Is the <li> inside the <a>?

Try this, http://api.drupal.org/api/drupal/includes--theme.inc/function/theme_links/7:

function THEMENAME_links__system_MENUNAME_menu($variables) {
  $output = '';
  foreach ($variables['links'] as $link) {
    $output .= l(<li' . drupal_attributes(array('class' => $class)) . '>' .'<span>'. check_plain($link['title']) .'</span>' . '</li>', $link['href'], $link);
  }
  return $output;
}

Is the <li> inside the <a>?

Try this, http://api.drupal.org/api/drupal/includes--theme.inc/function/theme_links/7:

function THEMENAME_links__system_MENUNAME_menu($variables) {
  $output = '';
  foreach ($variables['links'] as $link) {
    $output .= l(<li' . drupal_attributes(array('class' => $class)) . '>' .'<span>'. check_plain($link['title']) .'</span>' . '</li>', $link['href'], $link);
  }
  return $output;
}

Is the <li> inside the <a>?