This is an important study concerned with the development of the concepts and methods of classical stability theory in reference to the problems of singularly perturbed class systems. The various aspects of complex system dynamics are considered. Methods of the modelling and analysis on the generalized methodology basis, combining the stability theory ideas and asymptotic theory manners, are elaborated. Non-traditional extended approach, formed on Lyapunov's methods, Chetayev's stability postulate and the singularity postulate, is worked out. It gives a universal tool that makes it possible to come close to solving fundamental problems in general stability theory for singular systems dynamics, including decomposition problem. Here generalized statements and stability problems for singularly perturbed class systems are considered. The matter of investigation is the object, for which the original mathematical models are presented in a standard form of singularly perturbed systems with parametric perturbations of non-regular type. The critical transcendental cases (in the Lyapunov sense), that are generated by applied problems of Mechanics are examined. Besides, the systems with peculiarities inherent for mechanical systems are considered: there is no uniform asymptotic stability property; the perturbed system is close to the boundary of stability domain; generating systems are non-limit, singular ones; the nominal systems are quasi-Tikhonov's ones (on N.N. Moiseev). The reduction conditions are determined, and under the stability problem for the original system is reduced to the investigation of a shortened, approximate system of a less order; moreover, in the general case, this shortened system is a singular one (in sense of A.N. Tikhonov, S. Campbell). It is obtained by the solution of singularly perturbed problem of stability for cases, when the spectra of corresponding matrices are critical (with zero real parts of eigenvalues both for slow and for fast variables). Regular algorithms for estimating the parameter values, permitting the reduction in stability problem, are constructed. The results are discussed, which give strong substantiation of reduction principle for considered class systems. The received results are generalizing and supplementing ones that are known in the stability and the perturbation theory; and these new results are interesting both for theory and for theoretical and engineering applications.