  We prove existence of small amplitude, $2\pi \slash \om$-periodic in time
solutions of completely resonant nonlinear wave equations with Dirichlet
boundary conditions, for any frequency $ \om $ belonging to a Cantor-like set
of positive measure and for a new set of nonlinearities. The proof relies on a
suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser
Implicit Function Theorem. In spite of the complete resonance of the equation
we show that we can still reduce the problem to a {\it finite} dimensional
bifurcation equation. Moreover, a new simple approach for the inversion of the
linearized operators required by the Nash-Moser scheme is developed. It allows
to deal also with nonlinearities which are not odd and with finite spatial
regularity.
