Аннотация:In some of his previous papers the author generalized Lyapunov’s direct method to systems with small parameters [see Usp. Mat. Nauk 35, No.1(211), 127-170 (1980; Zbl 0429.34053)]. Here a survey is given on the further development and applications of this generalization. It deals with the stability in the critical case, partial stability properties, stability of integro-differential systems and multi-frequency systems.