  The scalar contributions to the radiative decays of light vector mesons into
a pair of neutral pseudoscalars, $V\to P^0P^0\gamma$, are studied within the
framework of the Linear Sigma Model. This model has the advantage of
incorporating not only the scalar resonances in an explicit way but also the
constraints required by chiral symmetry. The experimental data on
$\phi\to\pi^0\pi^0\gamma$, $\phi\to\pi^0\eta\gamma$, $\rho\to\pi^0\pi^0\gamma$
and $\omega\to\pi^0\pi^0\gamma$ are satisfactorily accommodated in our
framework. Theoretical predictions for $\phi\to K^0\bar K^0\gamma$,
$\rho\to\pi^0\eta\gamma$, $\omega\to\pi^0\eta\gamma$ and the ratio $\phi\to
f_0\gamma/a_0\gamma$ are also given.
