In the present work, we pay attention to a number of nonlinear Volterra integro-differential equations (VIDEs) with constant time-lag. We define three new Lyapunov functionals (LFs) and employ them to get specific conditions guaranteeing the uniform exponential asymptotic stability (UEAS) of the trivial solutions of the (VIDEs) considered. The results obtained generalize, compliment and improve the existing results in the literature from the cases of the without delay to the more general cases with time-lag.