  Together with the existence of new neutral gauge bosons, models based on
extended gauge groups (rank $> 4$) often predict also new charged fermions. A
mixing of the known fermions with new states with {\it exotic} weak-isospin
assignments (left-handed singlets and right-handed doublets) will induce tree
level flavour changing neutral interactions mediated by $Z$ exchange, while if
the mixing is only with new states with {\it ordinary} weak-isospin
assignments, the flavour changing neutral currents are mainly due to the
exchange of the lightest new neutral gauge boson $Z^\prime$. We show that the
present experimental limits on $\mu-e$ conversion in nuclei give a
nuclear-model-independent bound on the $Z$-$e$-$\mu$ vertex which is twice as
strong as that obtained from $\mu\to e e e$. In the case of E$_6$ models these
limits provide quite stringent constraints on the $Z^\prime$ mass and on the
$Z-Z^\prime$ mixing angle. We point out that the proposed experiments to search
for $\mu-e$ conversion in nuclei have good chances to find evidence of lepton
flavour violation, either in the case that new exotic fermions are present at
the electroweak scale, or if a new neutral gauge boson $Z^\prime$ of E$_6$
origin lighter than a few TeV exists.
