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 $\delta R_{\tau/K } =
\left(0.90_{\T - 0.26}^{\T + 0.17}\right) \%$.<BR>
For completeness we have also calculated the ratio of the electronic
and muonic decay modes of the pion.