Dependence of the gauge couplings on the moduli of the compactified space is studied for orbifold compactifications of the heterotic superstring. It is shown that such dependence is possible only for theories with sectors preserving N = 2 spacetime supersymmetry, and it satisfies a non-renormalization theorem. Namely, it is given entirely at the one-loop level and is determined by the violation of the integrability of 0-angle with respect to the moduli. (author). 23 refs.