In this paper, we defined exponential stability for nonlinear time-delay systems with delayed impulses. We derive the Lyapunov-based sufficient conditions for exponential stability. We show that the nonlinear impulsive time-delay system without impulse input delays is exponentially stable under the conditions. It is shown that the stable nonlinear impulsive time-delay system. It is a magnitude of the delayed impulses is sufficiently small, under the same conditions. The delayed impulses do not destroy the stability of the sizes of the impulse input delays.