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The width of the decay $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\omega}\ensuremath{\nu}$ is calculated in the framework of an extended Nambu-Jona-Lasinio model. The contributions of intermediate $\ensuremath{\rho}(770)$ and ${\ensuremath{\rho}}^{\ensuremath{'}}(1450)$ vector mesons are taken into account. The computed partial width and spectral function of this decay are found to be in a satisfactory agreement with experimental data.

The widths of the decays ${\ensuremath{\rho}}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}}){\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\nu}$ are calculated in the framework of the Nambu--Jona-Lasinio model. It is shown that these decays are defined by the $u$ and $d$ quark mass difference. It leads to the suppression of these decays in comparison with the main decay modes. In the process ${\ensuremath{\rho}}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\pi}}^{\ensuremath{-}}$ the intermediate scalar ${a}_{0}^{\ensuremath{-}}$ state is taken into account. For the $\ensuremath{\tau}$ decays the intermediate states with ${a}_{0}^{\ensuremath{-}}$, ${\ensuremath{\rho}}^{\ensuremath{-}}(770)$ and ${\ensuremath{\rho}}^{\ensuremath{-}}(1450)$ mesons are used. Our estimates are compared with the results obtained in other works.