Thank you.

But in this case - for once i found this out myself - it is much more simple:
MorphOS does recognize my monitor: Philips Brilliance 241B. But obviously assigns a wrong freqeuncy of 75Hz.

---> System: Prefs/Preferences/Monitors

Under monitor specifications my monitor is listed.
Choosing '24Bit 1920 x 1080' under Screen resolutions and then 'Edit....'.
And there a screen resolution of 1920 x 1080p (60hz) is available.
Test....Working!
Ok....Save....Restart.
And yes, it works! :)

I have only one question:
What is the difference between '1920x1080p(60hz)', '1920x1080 (60hz)' and '1920x1080(60hz)CVRB2'?