<script type="text/javascript"> 
var firstTracker = _gat._getTracker("UA-YYYYYYY-1"); 
firstTracker._initData(); 
firstTracker._trackPageview();

var secondTracker = _gat._getTracker("UA-ZZZZZZZ-1"); 
secondTracker._initData(); 
secondTracker._trackPageview(); 
</script> 

Thanks for your post!

In the Website I want to track I have the following code:

<script src="http://www.google-analytics.com/urchin.js" type="text/javascript"></script>
<script type="text/javascript">
_uacct = "UA-YYYYYYY-3";
_uacct = "UA-ZZZZZZZ-1";
urchinTracker();
</script>

</body>
</html>

I will substitute your code for my 6 current code lines above. Is that all I need to do?
I can't test it right now because I don't have FTP access with me.

Tanks a lot!

Adding the new tracking code [google.com]

There is a migration guide [google.com] on the analytics site, for converting more complicated tracking.

In the migration guide it shows an example of multiple tracking for the older version:

<script type="text/javascript">
_uacct = "UA-#*$!XX-X";
urchinTracker();
_uff = 0; // Reset flag to allow for second account
_uacct = "UA-#*$!XX-X";
</script>

I have never used the older version but I think there might be a typo. If the above code doesn't work I would try:

<script type="text/javascript">
_uacct = "UA-YYYYY-Y;
urchinTracker();
_uff = 0; // Reset flag to allow for second account
_uacct = "UA-ZZZZZ-Z;
urchinTracker();
</script>

Welcome to Webmasterworld BTW.