@Markiyan Hirnyk Thank you for your answer. I didn't really think much about the occuring numbers and didn't know that frequencyscale = relative was the default value. That one can increase the information level will help me to answer some question, I might have in the future.

@Markiyan Hirnyk That looks good. I take a closer look at it after I have installed DirectSearch.

@Preben Alsholm Thanks for your answer. I decided against giving too many details because I thought they would lead to solutions fit for my problem but not for similiar problems.
I take it, that you don't know how to make Maple consider a condition when evaluating NonlinearFit. Here some details, I hope that they help you: assume_in_Fit.mw

@Axel Vogt The file can be found (as I mentioned in the text) attached, you just have to click the link in the end.

@accer and Carl Love: Thanks for your answers.