The monograph outlines new methods for investigating degenerate problems of the theory of optimal processes associated with special controls and sliding modes. Such tasks are often found in problems of space navigation, flight dynamics, etc. The maximum principle and many other known methods are ineffective in investigating degenerate problems. Questions are considered: apparatus of Poisson brackets for calculating special controls, variations of conjugate systems, packages of variations, matrix pulses, connection between optimality criteria, optimal conjugation of control sections, etc. The book is designed for specialists involved in management tasks, as well as for undergraduate and graduate students of the departments of applied mathematics of universities.