  A detailed and general study of the fermionic structure of the 331 models
with \beta arbitrary is carried out based on the criterion of cancellation of
anomalies. We consider models with an arbitrary number of lepton and quark
generations, but requiring to associate only one lepton and one quark SU(3)
_{L} multiplet for each generation, and at most one right-handed singlet per
each left-handed fermion. We see that the number of quark left-handed
multiplets must be three times the number of leptonic left-handed multiplets.
Furthermore, we consider a model with four families and \beta =-1/\sqrt{3}
where the additional family corresponds to a mirror fermion of the third
generation of the Standard Model. We also show how to generate ansatzs about
the mass matrices of the fermions according to the phenomenology. In
particular, it is possible to get a natural fit for the neutrino hierarchical
masses and mixing angles. Moreover, by means of the mixing between the third
quark family and its mirror fermion, a possible solution for the A_{FB}^{b}
discrepancy is obtained.
