  The nonadiabatic effects due to the breakdown of Migdal's theorem in
high-$T_c$ superconductors are strongly affected by the opening of the
superconducting gap. Here we report how the momentum-frequency dependence of
vertex corrections is modified by the gap. A general effect is that the
positive region of the vertex corrections is increased leading to an
enhancement of their relevance. This has a number of physical consequences that
we discuss in details in relation to specific experiments.
