Thanks a lot. Meanwhile we did some tests which maybe indicate that the problem is the .htaccess / how MODx performs the rewrite.
We put a file including this code once in the modx-folder and once in none-modx-folder
<?
phpinfo();
?>
The output of the file in the modx-folder contains additional lines at different places:
containing HTTP_COOKIE PHPSESSID=7sdfasdfsf...
This means it is not a problem of the server or php.ini
It must be based somewhere in MODx
Maybe we have to give more writing-right with CHMOD to certain folders or files to not force MODx to deliver the session id in the URL? What do you think?
Gerdi