  The supersymmetric models extending the minimal supersymmetric standard model
(MSSM) by an additional Abelian gauge factor U(1)' in order to solve the mu
problem do generically suffer from anomalies disrupting the gauge coupling
unification found in the MSSM. The anomalies are absent if the minimal matter
content necessitated by the mu problem is augmented with exotic matter species
having appropriate quantum numbers. Recently, it has been shown that anomaly
cancellation can also be accomplished by introducing family non-universal U(1)'
charges and non-holomoprhic soft-breaking terms. We discuss collider signatures
of anomaly-free family non-universal U(1)' model by analyzing dilepton
production in future colliders. We find that, both at LHC and NLC, one can
establish existence/absence of such a Z' boson by simply comparing the number
of dilepton production events for electron, muon and tau lepton. The signal is
free of the SM background.
