  We investigate the semileptonic decays of B and D mesons into $\pi$ and
$\rho$ mesons, respectively, by means of QCD sum rules. We find that for the
vector formfactors involved the pole dominance hypothesis is valid to good
accuracy with pole masses in the expected range. Pole dominance, however, does
not apply to the axial formfactors which results in specific predictions for
the predominant polarization of the $\rho$ meson and the shape of the lepton
spectrum. For the total decay rates we find $\Gamma (\bar B^0 \to \pi^+ e^-
\bar\nu) = (5.1\pm 1.1)\,|V_{ub}|^2\, 10^{12}\,{\rm s^{-1}}$, $\Gamma ( D^0 \to
\pi^- e^+ \nu) = (8.0\pm 1.7)\,|V_{cd}|^2\, 10^{10}\,{\rm s^{-1}}$, $\Gamma
(\bar B^0 \to \rho^+ e^- \bar\nu) = (1.2\pm 0.4\,)\,|V_{ub}|^2\, 10^{13}\,{\rm
s^{-1}}$ and $\Gamma (D^0 \to \rho^- e^+\nu) = (2.4\pm 0.7)\,|V_{cd}|^2\,
10^{9}\,{\rm s^{-1}}$.
