  In the limit of small couplings in the nearest neighbor interaction, and
small total energy, we apply the resonant normal form result of a previous
paper of ours to a finite but arbitrarily large mixed Fermi-Pasta-Ulam
Klein-Gordon chain, i.e. with both linear and nonlinear terms in both the
on-site and interaction potential, with periodic boundary conditions. An
existence and orbital stability result for Breathers of such a normal form,
which turns out to be a generalized discrete Nonlinear Schr\"odinger model with
exponentially decaying all neighbor interactions, is first proved. Exploiting
such a result as an intermediate step, a long time stability theorem for the
true Breathers of the KG and FPU-KG models, in the anti-continuous limit, is
proven.
