Add some html in a menu I try to add some html in "secondary nav". 

A little bit like that :

    &lt;ul&gt;
      &lt;li&gt;
        &lt;div&gt;
          MY CUSTOM HTML
        &lt;/div&gt;
      &lt;/li&gt;
      &lt;li&gt;&lt;a&gt;First link&lt;/a&gt;&lt;/li&gt;
      &lt;li&gt;&lt;a&gt;Second link&lt;/a&gt;&lt;/li&gt;
    &lt;/ul&gt;


(my menu is not a block). 

Do you know how can it be done? By template suggestion or a function for example?
For menus that are printed by invoking theme('links__YOUR_MENU'), you can use the following code and place it in your theme's template.php file:

function YOUR_THEME_links__system_main_menu(&amp;$variables) {
  // Copy here the code from theme_links() function and adjust it to your liking.
}


See the source for theme_links() here.

For menus in blocks, you can do that using theme_menu_tree__YOUR_MENU() override in your theme's template.php file. Here's example code that will work for the main menu:

function YOUR_THEME_menu_tree__main_menu(&amp;$variables) {
  $your_custom_html  = '&lt;li&gt;&lt;div&gt;your custom HTML&lt;/div&gt;&lt;/li&gt;';
  return '&lt;ul class="menu clearfix"&gt;' . $your_custom_html . $variables['tree'] . '&lt;/ul&gt;';
}


This will add the content before menu links.