  In the extended Nambu--Jona-Lasinio model, the decay widths of the processes
$\tau \to [\omega(782), \phi(1020)] K^{-} \nu_{\tau}$ were calculated. The
intermediate channels with axial vector ($K_{1}(1270)$, $K_{1}(1400)$ and
$K_{1}(1650)$), vector ($K^{*}(892)$ and $K^{*}(1410)$) and pseudoscalar ($K$
and $K(1460)$) mesons were considered. The results for these processes are in
satisfactory agreement with the experimental data.
