  Production of $\rho(770)$, $\eta$ pairs at colliding of electron-positron
beams and in the decays $\rho(1450)\rightarrow \rho(770)\eta$, $\tau\rightarrow
\rho(770)\eta\nu_{\tau}$ is calculated in the framework of the Nambu -
Jona-Lasinio model. In the process of electron-positron annihilation and the
$\tau$ - lepton decay the contributions of the intermediate $\rho(770)$ vector
meson in the ground and first radially excited state are taken into account.
The theoretical prediction for the decay $\tau\rightarrow
\rho(770)\eta\nu_{\tau}$ is given. The obtained results for other processes are
in satisfactory agreement with the experimental data.
