This thesis work is devoted to an analysis of dilepton signatures of family nonuniversal U(1)' model. We first provide a brief overview of Standard Model of particle physics and Supersymmetry then we give an introduction to basic concepts of Minimal Supersymmetric StandardModel (MSSM) and necessities to extend theMSSMwith additional symmetry groups. Later we review various existing U(1). models, then we discuss the effects and results of family non-universality in current and future colliders. The supersymmetric models extending theMSSMby an additional Abelian gauge factor U(1). in order to solve the . 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 . 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-holomorphic soft-breaking terms (Demir, et al. 2005) and keeping the matter content minimal without exotic particles. We discuss collider signatures of anomaly-free family non-universal U(1). model by analyzing dilepton production in future colliders. We notice that, both at LHC and NLC, one can establish existance (or absence) of such a Z. boson by simply comparing the number of dilepton production events for electron, muon and tau lepton (Hayreter 2007).