This report considers certain problems of testing nonparametric hypotheses concerning type of dynamical system and/or random excitation; the choice of the right hypothesis should be based on statistical analysis of random vibration data for the system under consideration. The problems considered include: distinguishing between randomly excited oscillations and self-excited oscillations perturbed by random disturbances; analysis of stochastic stability for linearized system basing on measurements of random vibrations in nonlinear system; detection of periodically-induced parametric oscillations in presence of random noise; distinguishing between vibrations, induced by parametrical and external periodic excitation in presence of random noise. Theoretical solutions of these problems are based on analytical expressions for probability densities of amplitudes, obtained as solutions of FPK-equations of theory of Markov processes. The criteria obtained were checked on analog computer; simulation on analog computer was used also for checking the possibility of extiapolation of these criteria to certain cases, for which the theoretical solutions could not be obtained.