  We obtain limits on the electromagnetic and weak dipole moments of the
tau-lepton in the framework of a Left-Right symmetric model (LRSM) and a class
of $E_6$ inspired models with an additional neutral vector boson $Z_\theta$.
Using as an input the data obtained by the L3 and OPAL Collaborations for the
reaction $e^+e^-\to \tau^+\tau^-\gamma$, we get a stringent limit on the LRSM
mixing angle $\phi$, $-1.66\times 10^{-3}< \phi<1.22\times 10^{-3}$, which in
turn induces bounds on the tau weak dipole moments which are consistent with
the bounds obtained recently by the DELPHI and ALEPH Collaborations from the
reaction $e^+e^-\to \tau^+\tau^-$. We also get similar bounds for the weak
dipole moments of the tau lepton in the framework of $E_6$ superstring models.
