  We calculate the radiative corrections to the decays $\tau\to M \nu_\tau$ and
$\pi \to l \nu_\l$, where the meson $M$ is $M=\pi$ or $K$ and the lepton $l$ is
$l = e$ or $\mu$. We perform a complete calculation, which includes internal
bremsstrahlung and structure dependent radiation in the radiative decays and
point meson, hadronic structure dependent and short distance contributions in
the virtual corrections. Our result for the radiative correction to the ratio
$\Gamma(\tau\to\pi\nu_\tau(\gamma))/ \Gamma(\pi\to\mu\nu_\mu(\gamma))$ is
$\delta R_{\tau/\pi} = \left(0.16_{\T - 0.14}^{\T+0.09}\right) \%$. For the
ratio $\Gamma(\tau\to K\nu_\tau(\gamma)) / \Gamma(K\to \mu\nu_\mu(\gamma))$, we
obtain $\delta R_{\tau/K } = \left(0.90_{\T - 0.26}^{\T + 0.17}\right) \%$. For
completeness we have also calculated the ratio of the electronic and muonic
decay modes of the pion.
