  Radiative decays $\pi^0({\pi^0}')\to\gamma+\gamma$,
${\pi^0}'\to\rho^0(\omega)+\gamma$, ${\rho^0}'(\omega')\to\pi^0+\gamma$, and
${\rho^0}'(\omega')\to{\pi^0}'+\gamma$ are considered in the framework of the
non-local SU(2)$\times$SU(2) NJL model. Radially excited mesons are described
with the help of polynomial form factor $f({k^\bot}^2)$, where $k^\bot$ is the
quark momentum transverse to the external meson momentum. In spite of mixing of
the ground and excited meson states in this model, the decay widths of
$\pi^0\to\gamma+\gamma$ and $\rho^0(\omega)\to\pi^0+\gamma$ are found to be in
good agreement with experimental data as in the standard local NJL model. Our
predictions for decay widths of radially excited mesons can be verified in
future experiments.
