  We investigate the density instabilities present in the infinite-U
Hubbard-Holstein model both at zero and finite momenta as well as the
occurrence of Cooper instabilities with a specific emphasis on the role of
long-range Coulomb forces. In carrying out this analysis a special attention is
devoted to the effects of the strong local $e$-$e$ interaction on the $e$-$ph$
coupling and particularly to both the static and dynamic screening processes
dressing this coupling. We also clarify under which conditions in strongly
correlated electron systems a weak additional interaction, e.g. a
phonon-mediated attraction, can give rise to a charge instability. In the
presence of long-range Coulomb forces, the frustrated phase separation leads to
the formation of incommensurate charge density waves.
  These instabilities, in turn, lead to strong residual scattering processes
between quasiparticles and to superconductivity, thus providing an interesting
clue to the interpretation of the physics of the copper oxides.
