  In this paper, one-dimensional (1D) nonlinear wave equations $u_{tt}
-u_{xx}+V(x)u =f(u)$, with periodic boundary conditions are considered; V is a
periodic smooth or analytic function and the nonlinearity f is an analytic
function vanishing together with its derivative at u=0. It is proved that for
``most'' potentials V(x), the above equation admits small-amplitude periodic or
quasi-periodic solutions corresponding to finite dimensional invariant tori for
an associated infinite dimensional dynamical system. The proof is based on an
infinite dimensional KAM theorem which allows for multiple normal frequencies.
