On stability of the solutions of a class of nonlinear delay systems

Consideration was given to a class of systems of nonlinear differential equations with retarded argument. It was assumed that in the absence of delay the zero solutions of the systems under study are asymptotically stable. Using the method of Lyapunov functions in the form of B. S. Razumikhin, it was proved that if the right-hand sides of these equations are free of the linear terms relative to the phase variables, then the asymptotic stability is retained for any delay.