A study of the three-family local gauge group SU (3) c ⊗ SU (3) L ⊗ U (1) X with right-handed neutrinos is carried out. We use the minimal scalar sector able to break the symmetry in a proper way and produce, at the same time, masses for the fermion fields. We embed the structure into a simple gauge group and, by using experimental results from the CERN LEP, SLAC linear collider and atomic parity violation data, we also constrain relevant parameters for the new neutral and charged currents. We discuss the mass spectrum for the gauge boson sector and for the spin 1/2 particles. With the use of discrete symmetries and the introduction of extra scalar fields, a consistent mass spectrum could be constructed.