Summary: We consider a further development of Painlevé’s theory, the existence, continuability and uniqueness of right-hand solutions of the differential equations of dynamics, and, under certain additional conditions, of the equations of motion of holonomic mechanical systems with sliding friction. In classical mechanics, acceleration is essentially defined as the right-hand derivative of velocity. Hence the most meaningful definition of the “solution of a differential equation” in problems of the dynamics of mechanical systems with sliding friction is that using the concept of right derivative.