In the article [2], a general statement was obtained on the stability of the motion of holonomic scleronomic systems in the sense of Lyapunov, based on the second Lyapunoz method. The proposed criterion does not need to determine the differential equations of motion, and instead of the Lyapunov function, it is sufficient to choose some function that depends only on one of the generalized coordinates. In this article, based on this method, we study the stability of the motion of nonholonomic systems.