One of my main objectives throughout my reserach work is the determination of robust stability charts. One important requirement is, that the computational algorithms should be reliable from engineering point of view and they have to be insensitive to fluctuation of parameters of the dynamic system. Furthermore, I will have to spot out, which parameter sensitivity is critical. I will give recommendations, which approximations are acceptable in the case of different systems. For the development of my algorithms the existing algorithms have to be analyzed and I will choose those, which can serve as a basis for our development.Taking into consideration the required accuracy for a given error limit and the necessary corresponding simplifications, I intend to form new, mathematically correct algorithms for the investigation of quasi-periodic systems. Still it is crutial to determine the convergence of the results, and these have to be compared to accurate time simulations. For the stability computations the development of new theories and methods is needed. My methods will not only be checked by simulation results, but I plan the validation with measurements on test rigs built for this purpose.