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The processes of electron-positron annihilation into $\pi^0\gamma$ and into$\pi'(1300)\gamma$ are considered within the NJL model. Intermediate vectormesons $\rho^0$, $\omega$, $\rho'(1450)$, and $\omega'(1420)$ are taken intoaccount. 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 receivedfor 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 energyregion 600 -- 1020 MeV.

Processes $e^+e^-\to\pi^0({\pi^0}')\gamma$ in the NJL model