  We have used an exact diagonalization technique to study the stability of the
$t-J$-Holstein and Hubbard-Holstein models under the influence of the
electron-phonon interaction. Previous results have been obtained using
frozen-phonon technique or introducing only a few dynamical phonon modes due to
the large Hilbert space. To check these results we have done exact
diagonalization in a small cluster (four sites) including all the phonon modes
allowed by symmetry. We compare our results with those obtained by using the
adiabatic approximation.
