  Fermi energies in fullerene compounds and cuprates are extremely small as
consequence of the small number of charge carriers and are comparable to the
phonon frequency scale. In this situation the conventional Migdal-Eliashberg
theory does not hold anymore and nonadiabatic effects need to be taken into
account. In previous studies, a generalization of Eliashberg theory in the
nonadiabatic regime has been proposed to calculate normal state properties and
the onset temperature $T_c$ of the superconductive phase. Here we extend the
nonadiabatic theory below $T_c$ where the opening of the superconducting order
parameter affects the nonadiabatic correction. The superconducting gap $\Delta$
is calculated in a self-consistent way. We find that large values of the ratio
$2 \Delta/T_c$ are obtained in the nonadiabatic theory by smaller
electron-phonon coupling $\lambda$ than in Migdal-Eliashberg theory. This
agrees with the picture that strong-coupling phenomenology can be achieved in
nonadiabatic theory by ``reasonable'' values of $\lambda$. We apply our
analysis to the case of the fullerene compounds.
