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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 quarkmodel. The contact channel and intermediate channels with axial-vector, vectorand pseudoscalar mesons are taken into account. It is shown that the strangescalar meson $K^*_0$ plays an important role in these processes in addition tothe intermediate vector meson $K^*$. The obtained results are in satisfactoryagreement with the recent experimental data within the experimental andtheoretical uncertainties.

The decays $\tau \to [K^- K^0 \pi^0, K^- K^+ \pi^-, K^0 \bar{K^0} \pi^-] \nu_{\tau}$ in the NJL quark model