  The theory of Raman scattering by the electron--phonon coupled system in
metals and heavily doped semiconductors is developed taking into account the
Coulomb screening and the electron--phonon deformation interaction. The
Boltzmann equation for carriers is applied. Phonon frequencies and optic
coupling constants are renormalized due to interactions with carriers. The
$k-$dependent semiclassical dielectric function is involved instead of the
Lindhard-Mermin expression. The results of calculations are presented for
various values of carrier concentration and electron-phonon coupling constant.
