The book presents the results of the qualitative theory of differential equations of celestial mechanics obtained in the last decade. The book consists of two parts .. The first part deals with the methods of averaging differential equations of motion for multi-frequency mechanical systems, the mathematical substantiation of various averaging schemes in celestial mechanics. A significant place is occupied by the presentation of the results of N. N. Godly Love, V. M. Hair and Authors . Applications of the averaging method to the construction of analytical theories of asteroid motion in the case of resonant orbits. The second part is devoted to methods of constructing conditional-periodic solutions in the problems of celestial mechanics. Detailed results are given in . and . Arnold and Y. Moser . The wide possibilities of the method of accelerated convergence of the Newtonian type in celestial mechanics are illustrated by the application of general theorems to the unlimited and limited problems of three bodies. The book is intended for researchers, graduate students of senior courses in mathematics, mechanics and celestial mechanics. The book contains 12 drawings and 71 bibliographical references.