  In the extended Nambu-Jona-Lasinio model, the process of production of
charged kaon pair on colliding electron-positron beams in the energy interval 1
- 1.7 GeV is described. In studying of this process, we take into account the
contact terms when the pairs $K^{+}$ $K^{-}$ are generated by an intermediate
photon, and processes with intermediate vector mesons $\rho$, $\omega$ and
$\phi$ in the ground and in the first radially excited states. The results
obtained here are compared with experimental data recently received in
Novosibirsk and in Stanford.
