The effects of an extra Z ′ gauge boson with family nonuniversal fermion couplings on the rare top quark decay t → cγ are first examined in a model independent way and then in the minimal 331 model. It is found that the respective branching fraction is at most of the order of 10 −8 for m Z ′ = 500 GeV and dramatically decreases for a heavier Z ′ boson. This results is in sharp contrast with a previous evaluation of this decay in the context of topcolor assisted technicolor models, which found that B(t → cγ) ≃ 10 −6 for m Z ′ = 1 TeV. [6]. Quite recently, the CDF collaboration used the Fermilab Tevatron data to search for new massive neutral particles decaying into lepton pairs [7]. As far as new gauge bosons are concerned, they considered a new SM-like) and the one from the littlest Higgs model (Z H ) . The following lower bounds were obtained [7] for the masses of Z ′ SM , Z χ , Z ψ , Z η and Z I : 825, 690, 675, 720 and 615 GeV, whereas m ZH was found to be larger than 885, 860 ,805 and 725 GeV for the following values of the mixing parameter cotθ H : 1.0, 0.9, 0.7 and 0.5, respectively.If the couplings of the Z ′ to the fermions are assumed to be family universal, there is no flavor changing neutral current (FCNC) effects mediated by this particle even if there is fermion flavor mixing via the GIM mechanism. Nevertheless, it is possible that the Z ′ couples nonuniversally to the fermions, thereby giving rise to FCNCs. For instance, some theories require that the Z ′ couplings to the third family fermions are different than the ones to the fermions of the first two families. This is the case of the Z ′ predicted by the 331 model [8], which is based on the SU (3) L × U (1) X symmetry and has attracted considerably attention recently [9]. This model is particularly appealing due to its unique mechanism of anomaly cancelation: instead of the usual cancelation between each fermion family, it is necessary that all the three fermion families are summed over, which automatically requires the existence of a number of families that is multiple of 3. It has been conjectured that this may provide a hint to the solution of the family number problem. There are thus good motivations for an extra Z ′ boson, with a mass in the range 500 GeV-1 TeV, which couples nondiagonally to the fermions.Although the phenomenology of a Z ′ gauge boson is interesting by itself, so is the study of FCNC effects as they would be a hint of new physics because of their large suppression in the SM. This class of effects has been considerably studied in the literature via some rare decay modes of the top quark. The interest in the top quark phenomenology stems from its large mass, which has led to some belief that new physics effects are more likely to show through processes involving this particle. Even more, the copious production of top quark pairs at the CERN large hadron collider (LHC) will allow us to examine several top quark properties and some of its rare decays. It is thus very interesting to consider the virtual effects of a Z ′ gauge ...