  Using 3.3 pb$^{-1}$ of data collected with the CMD-2 detector in the 720 --
840 MeV c.m. energy range, the branching fraction of the conversion decay
$\omega\to\pi^0e^+e^-$ has been measured:
$\mathcal{B}(\omega\to\pi^0e^+e^-)=(8.19\pm0.71\pm0.62)\cdot10^{-4}$. The upper
limits for the branching fractions of the following conversion decays have been
obtained at the 90% confidence level:
$\mathcal{B}(\rho\to\pi^0e^+e^-)<1.6\cdot10^{-5}$, $\mathcal{B}(\rho\to\eta
e^+e^-)<0.7\cdot10^{-5}$ and $\mathcal{B}(\omega\to\eta
e^+e^-)<1.1\cdot10^{-5}$.
