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We continue to study an infinite-parametric family of gauge theories with anarbitrary function of the self-dual part of the field strength as theLagrangian. The arising one-loop divergences are computed using the backgroundfield method. We show that they can all be absorbed by a local redefinition ofthe gauge field, as well as multiplicative renormalisations of the couplings.Thus, this family of theories is one-loop renormalisable. The infinite set ofbeta-functions for the couplings is compactly stored in a renormalisation groupflow for a single function of the curvature. The flow is obtained explicitly.

One-loop beta-function for an infinite-parameter family of gauge theories