This paper deals with the regularity for the nonlinear\nintegrodifferential equations governed by the variational inequality\nin Hilbert spaces, and a variation of constant formula for\nsolutions is established. It is to extend the regularity for solutions of second order variational inequalities to the nonlinear variational inequalities of hyperbolic type with nonlinear perturbations on condition of the Lipschitz continuity of the nonlinear terms. A simple example to which our main result can be applied is given.