Summary: In order to describe control systems with variable structure, a hierarchical two-level model with a discrete time dynamical model at the upper level and a continuous time differential model with homogeneous structure at the lower level is considered. New sufficient optimality conditions which generalize those developed earlier by V. F. Krotov and the author [Methods and problems of optimal control (Russian) (1973; Zbl 0271.49003)], and the author [Principle of extension of control problems (Russian) (Moscow 1985)], for such systems are proposed. In these conditions at each level the Krotov function is replaced by a resolving system which consists of a family of Krotov-type functions and a functional over this family. A brief review of earlier theoretical and applied results is given.