  The axion solution to the strong CP problem makes use of a global
Peccei-Quinn U(1) symmetry which is susceptible to violations from quantum
gravitational effects. We show how discrete gauge symmetries can protect the
axion from such violations. PQ symmetry emerges as an approximate global
symmetry from discrete gauge symmetries. Simple models based on Z_N symmetries
with N =11,12, etc are presented realizing the DFSZ axion and the KSVZ axion.
The discrete gauge anomalies are cancelled by a discrete version of the
Green-Schwarz mechanism. In the supersymmetric extension our models provide a
natural link between the SUSY breaking scale, the axion scale, and the
SUSY-preserving \mu term.
