  We extend the gauge coupling of Super-Yang-Mills theories to an external
superfield composed out of a chiral and an antichiral superfield and perform
renormalization in the extended model. In one-loop order we find an anomalous
breaking of supersymmetry which vanishes in the limit to constant coupling. The
anomaly arises form non-local contributions and its coefficient is gauge and
scheme independent and strictly of one-loop order. In the perturbative
framework of the construction the anomaly cannot be absorbed as a counterterm
to the classical action. With local gauge coupling the symmetric counterterms
with chiral integration are holomorphic functions and this property is
independent from the specific regularization scheme. Thus, the symmetric
counterterm to the Yang-Mills part is of one-loop order only - and it is the
anomaly which gives rise to the two-loop order of the gauge $\beta$-function in
pure Super-Yang-Mills theories and to its closed all-order expression.
