  Small size QCD instantons may spoil the axion solution to the strong CP
problem if QCD is not asymptotically free at high energy scales. We examine
this issue in supersymmetric models using a manifestly supersymmetric scheme to
compute the axion potential induced by small size instantons. Applying this
scheme for a class of illustrative models, it is found that the resulting high
energy axion potential is highly model-dependent, but suppressed by more powers
of the soft supersymmetry breaking parameters and/or of the other small mass
scales than what is expected based on a naive instanton graph analysis. Our
analysis suggests that the axion solution is stable against the small QCD
instanton effects in a wide class of supersymmetric models even when QCD is not
asymtotically free at high energy scales.
