  The processes of electron-positron annihilation into $\pi^0\gamma$ and into
$\pi'(1300)\gamma$ are considered within the NJL model. Intermediate vector
mesons $\rho^0$, $\omega$, $\rho'(1450)$, and $\omega'(1420)$ are taken into
account. The latter two mesons are treated as the first radial excited states.
They are incorporated into the NJL model by means of a polynomial form factor.
Numerical predictions for the cross sections of these processes are received
for the center-of-mass energies below 2 GeV. Our results for the $\pi^0\gamma$
production are in agreement with experimental data received in the energy
region 600 -- 1020 MeV.
