Now I know the problem. After installing Avahi Zeroconfig Browser on my Ubuntu I realized, that mdns still running. Then I connected my MacBook Pro with an ethernet cable instead of the wireless connection and it works like a charm. Now I guess, it comes from my Netgear WLAN router. Maybe I find a way to fix this.
Ah, yeah… my dad had the same problem with his netgear. Updating the firmware fixed it.
I updated the firmware earlier today and now it works!