You would have to edit the file tpl_ezpages_bar_header.php in includes\templates\YOUR_TEMPLATE\templates in order to generate the link with the correct CSS-class.

Example: Add this after the last include, after line 18.

Code:
<?php 
$akt_seite= htmlspecialchars('http://'.$_SERVER['SERVER_NAME'].$_SERVER['REQUEST_URI']);
?>
This code will tell your php-script, which page is loaded by the client.

Then you have to find the line, where the links are generated and add a if-statement for the class="xxx". The if-statement will compare the actualy loaded page with the url in the link.

Example:

Code:
  <div <?php if($akt_seite != $var_linksList[$i]['link']) echo 'class="topLink"'; else echo 'class="topLinkActive"'; ?> ><a href="<?php echo $var_linksList[$i]['link']; ?>"><?php echo $var_linksList[$i]['name']; ?></a></div>
The original code would create a <ul> and <li>, I do use <div>, but you should be able to integrate this with <ul><li> too.

Well, this way you can now create the two needed CSS classes. Example: .topLink a{color: grey;} and .topLinkActive a{color: blue;} -> for <ul><li> figure it out by yourself.

I guess that I will have to edit other files too, as there are links generated in other places too. But now you know how to do this.