In this paper we consider finite element methods for nonlinear hyperbolic integro-differential problems defined in ${Omega};{subset};R^d(d;{leq};4)$. A new initial approximation of $u_t(0)$ is taken. Optimal order error estimates in $L_p$ for $2;{leq};p;{leq};{infty}$ are established for arbitrary order finite element. One order superconvergence in $W^{1,p}$ for $2;{leq};p;{leq};{infty}$ are demonstrated as well.