Extra Neutral Gauge Boson from Two Versions of the 3-3-1 Model in Future Linear Colliders

Our aim is to establish some signatures of the extra gauge boson ${Z^\prime}$, predicted in two versions of ${SU (3)_C \times SU (3)_L \times U (1)_X}$ model and to show possible differences between these signatures. First, by considering the process $e^+ + e^- \longrightarrow \mu^+ +\mu^- $, we obtain some observables and next, by considering additional hadronic final states, we obtain lower bounds for $M_{Z^\prime}$, within 95% C.L.. We also include our preliminary results concerning $p \bar p$ and $p p$ collisions in order to support our conclusions about the possibility to discriminate the various versions of 3-3-1 model. From our analysis we conclude that linear colliders can show a clear signature for the existence of $Z^\prime$ predicted in the 3-3-1 model and also that it can discriminate the versions.