  Generation dependent discrete symmetries often appear in models derived from
superstring theories. In particular, in the framework of E$_6$ models the
presence of such symmetries is required in order to allow for the radiative
generation of naturally small neutrino masses. Recently it was shown that by
imposing suitable generation dependent discrete symmetries, a class of models
can be consistently constructed in which the three sets of known fermions in
each generation do not have the same assignments with respect to the {\bf 27}
representation of E$_6$. In this scenario, the different embedding in the gauge
group of the three generations implies in particular that the known charged
leptons couple in a non--universal way to the new neutral gauge bosons
$(Z_\beta)$ present in these models. We exploit this fact to study the
signature of this class of models at present and future $e^+e^-$ colliders. We
show that some signals of deviation from lepton universality as well as some
other discrepancies with the standard model predictions which have been
observed at the TRISTAN collider in the production rate of $\mu$ and $\tau$,
can be accounted for if the $Z_\beta$ mass is not much heavier than 300 GeV. We
also study the discovery limits for lepton universality violation of this type
at LEP-2 and at the 500 GeV $e^+e^-$ Next Linear Collider (NLC). We show that
models predicting unconventional assignments for the leptons will give an
unmistakable signature, when the $Z_\beta$ mass is as heavy as $\sim 800$ GeV
(LEP-2) and $\sim 2$ TeV (NLC).
