  We obtain bounds on the anomalous magnetic and electric dipole moments of the
tau-neutrino through the reaction $e^{+}e^{-}\to \nu \bar \nu \gamma$ at the
$Z_1$-pole in the framework of a Left-Right symmetric model and a class of
$E_6$ inspired models with an additional neutral vector boson $Z_\theta$. We
use the data collected by the L3 Collaboration at LEP. For the parameters of
the $E_6$ model we consider the mixing angle $\theta_{E_6}=37.8^o$ and
$M_{Z_\theta}=7M_{Z_1}$. We find that our bounds are of the same order of
magnitude as those obtained in other extensions of the Standard Model.
