Our aim is to establish some signatures of the extra gauge boson Z ′, predicted in two versions of the SU(3)C× SU(3)L×U(1)X model and to show possible differences between these signatures. First, by considering the process e++e -→μ++μ-, we obtain some observables and next, by considering additional hadronic final states, we obtain lower bounds for MZ′, within 95% C.L. We also include our preliminary results concerning pp̄ and pp collisions in order to support our conclusions about the possibility to discriminate different versions of the 3-3-1 model. From our analysis we conclude that linear colliders can show a clear signature for the existence of Z′ predicted in the 3-3-1 model and also that it can discriminate the various versions. © Springer-Verlag Berlin Heidelberg 2007.