Dear Peter, thanks for Your reply!
The license repair app occures in the dock, but doesn't start.
What else could I do?
Reboot and try it again. Beyond that, I don't know. Google might come up with some similar threads with other workarounds, but as far as I know if you get the "Licensing has stopped working" error in CS4, the repair tool is the only thing that can fix it. Reinstall might work, but very will might not.