  The Peccei-Quinn symmetry is an automatic symmetry of the 3-3-1 gauge models
which, consequently are not plagued with the strong CP problem. Nevertheless,
the axion that emerges from spontaneous breaking of Peccei-Quinn symmetry
cannot be made invisible in the original versions of these models, unless we
extend their scalar sector by an additional neutral scalar singlet. In this
case we show that if, we also add heavy neutrinos in the singlet form, we get
to solve three interesting open questions at once: the real component of the
neutral scalar singlet driving inflation, the axion playing the role of the
dark matter of the universe and standard neutrinos gaining masses through
seesaw mechanism.
