  We discuss a 331 model with three scalar triplets and neutral fermion
singlets. We show that in the 331 model with right-handed neutrinos, it is
possible to obtain small active neutrino masses via the double and inverse
seesaw mechanisms, without the use of scalar sextets or triplets with
doubly-charged Higgs. Two types of models are discussed. If we have a large
Majorana mass matrix for the singlets, the spectrum of neutrinos presents
light, heavy and very heavy masses. The other possibility is a small (zero)
Majorana mass matrix, which leads to pseudo-Dirac (Dirac) heavy neutrinos in
the TeV scale, in addition to the active light neutrinos
