  The branching fractions of the decays $\tau \to a_{1} \pi \nu_\tau$, $\tau
\to K_{1} \pi \nu_\tau$ and $\tau \to K_{1} K \nu_\tau$ are calculated in the
framework of the extended $U(3)\times U(3)$ chiral Nambu--Jona-Lasinio model.
There are no experimental data for these decays in the present time, thus the
obtained results are considered as predictions. The comparison of these results
to the theoretical results of other authors is carried out.
