  We examine the influence of gauge kinetic mixing on the couplings of a TeV
scale $Z'$ in both $E_6$ and SO(10) models. The strength of such mixing, which
arises due to the existence of incomplete matter representations at low scale,
can be described by a single parameter, $\delta$. The value of this parameter
can significantly influence the ability of both hadron and lepton colliders to
detect a $Z'$ using conventional search techniques. In addition, $\delta \neq
0$ also adds to the complexities involved in separating $E_6$ $Z'$ models from
those arising from alternative scenarios. Employing a reasonable set of
assumptions we have determined the allowed range for this parameter within a
wide class of models via an RGE analysis. In particular, given the requirements
of Standard Model gauge coupling unification, anomaly freedom and
perturbativity up to the GUT scale, we demonstrate that the necessary condition
for exact leptophobia in $\eta$ type $E_6$ models, $\delta=-1/3$, is impossible
to achieve in this scenario. Furthermore we show that the allowed range for
$\delta$ is rather restricted for arbitrary values of the mixing between the
$U(1)_\chi$ and $U(1)_\psi$ type couplings. The SO(10) $Z'$ model $\chi$ is
discussed as a separate case since it requires special attention.
