  The infinite mass effective theory, when a heavy quark mass tends to
infinity, and Chiral perturbation theory at the quark level, based on the
extended Nambu -- Jona -- Lasinio model with linear realization of chiral
$U(3)\times U(3)$ symmetry, are applied to the calculation of current $s$ --
quark mass corrections to the form factors of the $D\to\bar K~e^+~\nu_e$ and
$D\to\bar K^{\ast}~e^+~\nu_e$ decays. These corrections turn out to be quite
significant, of the order of $7-20\%$. The theoretical results are compared
with experimental data.
