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In the extended NJL model the total cross sections of the processes $e^+e^-\to (\eta, \eta', \eta(1295), \eta(1405))\gamma$ at energies up to 2 GeV arecalculated. The intermediate vector mesons $\rho (770)$, $\omega(782)$, $\phi(1020)$, $\rho' (1450)$, $\omega' (1420)$ and $\phi' (1680)$ are taken intoaccount. The latter three mesons are treated as the first radial excitedstates. They are incorporated into the NJL model by means of polynomial formfactors. The calculation results are in satisfactory agreement with theexperimental data obtained with the SND detector at the VEPP-2M, Novosibirsk.The predictions given for the process $e^+e^- \to (\eta',\eta(1295),\eta(1405)) \gamma$ have not been experimentally tested yet.

Processes of $e^+e^- \to (\eta, \eta', \eta(1295), \eta(1475))\gamma$ in the extended Nambu -- Jona-Lasinio model