  We consider 1D completely resonant nonlinear wave equations of the type
v_{tt}-v_{xx}=-v^3+O(v^4) with spatial periodic boundary conditions. We prove
the existence of a new type of quasi-periodic small amplitude solutions with
two frequencies, for more general nonlinearities. These solutions turn out to
be, at the first order, the superposition of a traveling wave and a modulation
of long period, depending only on time.
