This chapter consists of two parts. In the first part we present two theories of motion of nonholonomic systems with high-order (program) constraints. In the first theory, we construct a consistent system of differential equations for the unknown generalized coordinates and the Lagrange multipliers. The second theory is based on the generalized Gauss principle. In the second part, for one of the most principal problems of the control theory-the problem of optimal control force that transforms a given mechanical system in a given amount of time from one phase state into a different one–we employ the second theory. This allows one to construct a control force in the form of a polynomial of time. The application of this theory is illustrated on the model problem of oscillation suppression for a cart with pendulums. We pose and solve an extended boundary-value problem. Because of this, it proves possible to find a control force without jumps peculiar to solutions obtained via the Pontryagin maximum principle.