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We show that by introducing appropriate local $Z_N(N\geq13)$ symmetries inelectroweak models it is possible to implement an automatic Peccei-Quinnsymmetry keeping at the same time the axion protected against gravitationaleffects. Although we consider here only an extension of the standard model anda particular 3-3-1 model, the strategy can be used in any kind of electroweakmodel. An interesting feature of this 3-3-1 model is that if: {\it i)} we addright-handed neutrinos, {\it ii)} the conservation of the total lepton number,and {\it iii)} a $Z_2$ symmetry, the $Z_{13}$ and the chiral Peccei-Quinn$U(1)_{\rm PQ}$ are both accidental symmetries in the sense that they are notimposed on the Lagrangian but they are just the consequence of the particlecontent of the model, its gauge invariance, renormalizability and Lorentzinvariance. In addition, this model has no domain wall problem.Comment: Some changes and a new reference added, 7 page

Naturally light invisible axion in models with large local discrete symmetries