  Semileptonic decays $D\to K,K^*,\pi,\rho$, $D_s\to \eta,\eta',\phi$, and
$B\to D,D^*,\pi,\rho$ are analyzed within the dispersion formulation of the
quark model. The form factors at timelike $q$ are derived by the analytical
continuation from spacelike $q$ in the form factors of the relativistic
light--cone quark model. The resulting double spectral representations allow a
direct calculation of the form factors in the timelike region. The results of
the model are shown to be in good agreement with all available experimental
data. From the analysis of the $B\to D,D^*$ decays we find $|V_{cb}|=0.037\pm
0.004$, and the $B\to\pi,\rho$ decays give $|V_{ub}|=0.004\pm 0.001$.
