The strong-CP question in SU(3)_c X SU(3)_L X U(1)_N models

We analyze two recent models based on the gauge group SU(3)${}_c\times$SU(3)${}_L\times$U(1)${}_N$ where each generation is not anomaly-free, but anomaly cancels when three generations are taken into account. We show that the most general Yukawa couplings of these models admit of a Peccei-Quinn symmetry. This symmetry can be extended to the entire Lagrangian by using extra fields in a very elegant way so that the resulting axion can be made invisible.