We study the long-time behavior as time goes to infinity of global bounded solutions to the following nonautonomous semilinear viscoelastic equation: vertical bar u(t)vertical bar(rho)u(tt) - Delta u(tt) - Delta u(t) - Delta u +integral(tau)(0) k(s) Delta u(t - s) ds + f (x, u) = g, tau is an element of{t, infinity}, in , with Dirichlet boundary conditions, where is a bounded domain in and the nonlinearity f is analytic. Based on an appropriate (perturbed) new Lyapunov function and the Aojasiewicz-Simon inequality we prove that any global bounded solution converges to a steady state. We discuss also the rate of convergence which is polynomial or exponential, depending on the Aojasiewicz exponent and the decay of the term g.