[BRotondi]

If someone is interested in the solution:
Template navbar:
replace

        <ul class="navbar_advanced_search">
            <li><a href="search.php{vb:raw session.sessionurl_q}" accesskey="4">{vb:rawphrase advanced_search}</a></li>
        </ul>

e.g. with

        <ul class="navtabs floatcontainer">
            <li class="selected">&nbsp;
                <ul class="floatcontainer">
                    <li class="popupmenu">
                        <a href="javascript://" class="popupctrl" >{vb:rawphrase advanced_search}</a>
                        <ul class="popupbody popuphover">
                            <li><a href="search.php?{vb:raw session.sessionurl}search_type=1" accesskey="4">{vb:rawphrase advanced_search}</a></li>
                            <li><a href="http://www.google.ch/search?hl=de&q=SUCHE+site%3A{vb:raw vboptions.bbtitle}&btnG=Suche&meta=" rel="nofollow" target="_blank">Suchen via Google</a></li>
                            <li></li>
                            <li><a href="tags.php?tag=.Begriff" rel="nofollow">Begriffe</a></li>
                            <li><a href="search.php?{vb:raw session.sessionurl}do=finduser&u={vb:raw bbuserinfo.userid}">Eigene Beitr?ge</a></li>
                            <li><a href="search.php?{vb:raw session.sessionurl}do=finduser&u={vb:raw bbuserinfo.userid}&starteronly=1">Eigene Themen</a></li>
                            <li></li>
                            <li><a href="http://bibleserver.com" rel="nofollow" target="_blank">Bibel Online</a></li>
                            <li><a href="http://de.wikipedia.org/w/index.php?title=Spezial:Suche" rel="nofollow" target="_blank">Wikipedia</a></li>
                        </ul>
                    </li>
                </ul>
            </li>
        </ul>

and add to additional.css

/* Advanced Search-Pulldown */
.globalsearch li, 
.globalsearch li.selected {
    border: none;
}
.globalsearch ul {
    background: none;
    border: none;
}