  In this paper the statement of the second Bogolyubov's theorem on periodic
solutions of smooth systems with small parameter is justified for
discountinuous systems. It is assumed that the generating solution intersects
the discontinuity hyperplanes transversally and that the system is smooth
outside of these hyperplanes. Such a situation is natural for mechanical
systems with dry friction and without constraints and sticking of oscillations.
To illustrate the result we prove stability of the velocity of
vibration-induced displacement.
