The paper concerns about the asymptotic behaviour of so-lutions of initial boundary value problem for a general anisotropic vis-coelastic system in the form of integrodifferential sytem of equations with homogeneous mixed boundary condition. We put a usual assumption on the relaxation tensor and assume that the inhomogeneous term of the equation and boundary data are zero. Then, by using the energy method, we show that the solutions decays exponentially with respect to time as it tends to infinity.
