This paper considers the problem of optimal control of an object, whose motion is described by a system of ordinary differential equations. The original problem is reduced to the problem of unconstrained minimization of a nonsmooth functional. For this, the necessary minimum conditions in terms of subdifferential and hypodifferential are determined. A class of problems, for which these conditions are also sufficient, is distinguished. On the basis of these conditions, the subdifferential descent method and the hypodifferential descent method are applied to the considered problem. The application of the methods is illustrated by numerical examples. Refs 16. Tables 4.