  We point out that the cross-section for the process $e^+ e^- \to e^+ e^-
\tau^+ \tau^-$ at LEP is large enough to allow for a study of the anomalous
electromagnetic couplings of the $\tau$ lepton. We show that the present bounds
on the magnetic dipole moment can be improved and that competitive bounds can
be obtained for the electric dipole moment using the data taken from 1992 to
1994. Finally, we briefly discuss the improvements that can be obtained at LEP
II.
