  In the framework of the $U(3) \times U(3)$ extended Nambu-Jona-Lasinio model,
the processes $e^+e^- \to K^+K^-\pi^0$ and $e^+e^- \to K^+K^-\eta$ are
described taking into account both ground and first radially excited
intermediate meson states. It is shown that channels with radially excited
$\phi(1680)$ meson are dominant in both processes. The influence on the results
of the appearance of phase factors of radially excited intermediate states, the
existence of which is indicated by experimental data, is discussed.
