Ok I got it to work now.
You´re right. There was indeed no such css file. I re-installed the plugin again and when I activated it I got the following error:
Warning: fopen(........./wp-content/plugins/ajax-event-calendar/css/cat_colors.css) [function.fopen]: failed to open stream: Permission denied in ........../wp-content/plugins/ajax-event-calendar/ajax-event-calendar.php on line 1159
cannot open file
I guess that prevented the css file from being created.
However, even with all permissions set to 777 and creating cat_colors.css manually it still didn´t work.
So I re-installed it again (third time) and changed the permissions to CHMOD777 BEFORE activating your plugin. Only then the css file could be created automatically.
I´m not php nor server-stuff-savy but since it´s the very first plugin to ever do that I´m still not sure that it has something to do with any general faulty permission setting on my server.
Anyway...thanks for pointing me in the right direction.