  In the extended Nambu - Jona - Lasinio model the decay widths $\tau
\rightarrow \rho(770) (\rho'(1450)) \nu_\tau$ and $\tau \rightarrow K^{*}(892)
(K^{*'}(1410)) \nu_\tau$ are studied in the quark one -loop approximation. Our
estimations of the decay widths $\tau \rightarrow K^{*}(892) (K^{*'}(1410))
\nu_\tau$ are in satisfactory agreement with experimantal data. In the paper,
the decay widths $\tau \rightarrow \rho(770) (\rho'(1450)) \nu_\tau$ are also
calculated.
