  We show that there is an infinite number of U(1) symmetries like Peccei-Quinn
symmetry in the 3-3-1 model with minimal scalar sector---two scalar triplets.
Moreover, all of them are completely broken due to the model's scalars by
themselves (notice that these scalars as known have been often used to break
the gauge symmetry and generating the masses for the model's particles). There
is no any residual Peccei-Quinn symmetry. Because of the minimal scalar content
there are some quarks that are massless at tree-level, but they can get
consistent mass contributions at one-loop due to this fact. Interestingly,
axions as associated with the mentioned U(1)s breaking (including Majoron due
to lepton-charge breaking) are all gauged away because they are also the
Goldstone bosons responsible for the gauge symmetry breaking as usual.
