Setting the Unlit flag does not help.
For the moment there are no lights in the level only an ambient light from the sun, setting 25, 25, 25.
Only thing different with the two models; at first, for the right model, I had used material setup in manage skins. Later on I have removed that setting and assigned it with the material script.
This strange behaviour still exists and I have no clue how to solve this.
Only thing I can think of is, that I remake that model from scratch.