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 discusses methods for averaging differential equations of motion for multi-frequency mechanical systems, provides mathematical justification for various averaging schemes in celestial mechanics. A significant place is occupied by the presentation of the results of N.N. Bogolyubov, V.M. Volosov and the authors. Applications of the averaging method to the construction of analytical theories of the motion of asteroids in the case of resonant orbits are given. The second part is devoted to methods for constructing conditional periodic solutions in problems of celestial mechanics. A detailed presentation of the results of V.I. Arnold and Yu. Mozer is given. The wide possibilities of the method of accelerated convergence of the Newtonian type in celestial mechanics are illustrated in the application of general theorems to the unlimited and limited problems of three bodies. The book is designed for scientists, graduate students and senior students engaged in mathematics, mechanics and celestial mechanics.