  The $\tau$ lepton decays $\tau \to [K^- K^0 \pi^0, K^- K^+ \pi^-, K ^0
\bar{K^0} \pi^-] \nu_{\tau}$ are described in the $U(3) \times U(3)$ NJL quark
model. The contact channel and intermediate channels with axial-vector, vector
and pseudoscalar mesons are taken into account. It is shown that the strange
scalar meson $K^*_0$ plays an important role in these processes in addition to
the intermediate vector meson $K^*$. The obtained results are in satisfactory
agreement with the recent experimental data within the experimental and
theoretical uncertainties.
