  We propose two 3-3-1 models (with either neutral fermions or right-handed
neutrinos) based on S_3 flavor symmetry responsible for fermion masses and
mixings. The models can be distinguished upon the new charge embedding
(\mathcal{L}) relevant to lepton number. The neutrino small masses can be given
via a cooperation of type I and type II seesaw mechanisms. The latest data on
neutrino oscillation can be fitted provided that the flavor symmetry is broken
via two different directions S_3 \rightarrow Z_2 and S_3 \rightarrow Z_3 (or
equivalently in the sequel S_3 \rightarrow Z_2 \rightarrow Identity), in which
the second direction is due to a scalar triplet and another antisextet as small
perturbation. In addition, breaking of either lepton parity in the model with
neutral fermions or lepton number in the model with right-handed neutrinos must
be happened due to the \mathcal{L}-violating scalar potential. The TeV seesaw
scale can be naturally recognized in the former model. The degenerate masses of
fermion pairs (\mu, \tau), (c, t) and (s, b) are respectively separated due to
the S_3 \rightarrow Z_3 breaking.
