An efficient method is proposed for the multiharmonic frequency-domain analysis of the stability for nonlinear periodic forced vibrations in gas turbine engine structures and turbomachines with friction, gaps, and other types of nonlinear contact interfaces. The method allows using large-scale finite element models for structural components together with detailed description of nonlinear interactions at contact interfaces between these components. The highly accurate reduced models are applied in the assessment of stability of periodic regimes for large-scale model of gas turbine structures. An approach is proposed for the highly accurate calculation of motion of a structure after it is perturbed from the periodic nonlinear forced response. Efficiency of the developed approach is demonstrated on a set of test cases including simple models and large-scale realistic bladed disk models with different types of nonlinearities: friction, gaps, and cubic nonlinear springs.