ABSTRACT: We study the scalar potential and the mass spectrum of the supersymmetric extension of a three-family model based on the local gauge group SU(3)C⊗SU(3)L⊗U(1)X, with anomalies canceled among the three families in a nontrivial fashion. In this model the slepton multiplets play the role of the Higgs scalars and no Higgsinos are needed, with the consequence that the sneutrino, the selectron and six other sleptons play the role of the Goldstone bosons of the theory. By introducing an Abelian anomaly-free discrete symmetry and aligning the vacuum in a convenient way, we get a consistent mass spectrum for the scalars and for the spin 1/2 quarks and charged leptons, where only the top and charm quarks and the tau lepton acquire tree level masses while the remaining ordinary charged fermions acquire radiative hierarchical masses.