Asymptotic methods of nonlinear mechanics developed by N. M. Krylov and N. N. Bogoliubov originated new trend in perturbation theory. They pene trated deep into various applied branches (theoretical physics, mechanics, ap plied astronomy, dynamics of space flights, and others) and laid the founda tion for lrumerous generalizations and for the creation of various modifications of thesem. E!f,hods. A great number of approaches and techniques exist and many differen. t classes of mathematical objects have been considered (ordinary differential equations, partial differential equations, delay diffe,'ential equations and others). The stat. e of studying related problems was described in mono graphs and original papers of Krylov N. M. , Bogoliubov N. N. [1], [2], Bogoli ubov N. N [1J, Bogoliubov N. N. , Mitropolsky Yu. A. [1], Bogoliubov N. N. , Mitropol sky Yu. A. , Samoilenko A. M. [1], Akulenko L. D. [1], van den Broek B. [1], van den Broek B. , Verhulst F. [1], Chernousko F. L. , Akulenko L. D. and Sokolov B. N. [1], Eckhause W. [l], Filatov A. N. [2], Filatov A. N. , Shershkov V. V. [1], Gi acaglia G. E. O. [1], Grassman J. [1], Grebennikov E. A. [1], Grebennikov E. A. , Mitropolsky Yu. A. [1], Grebennikov E. A. , Ryabov Yu. A. [1], Hale J . K. [I]' Ha paev N. N. [1], Landa P. S. [1), Lomov S. A. [1], Lopatin A. K. [22]-[24], Lykova O. B.
