  We study systematically, through two loops, the divergence structure of the
supersymmetric WZ model defined on the N=1/2 nonanticommutative superspace. By
introducing a spurion field to represent the supersymmetry breaking term F^3 we
are able to perform our calculations using conventional supergraph techniques.
Divergent terms proportional to F, F^2 and F^3 are produced (the first two are
to be expected on general grounds) but no higher-point divergences are found.
By adding ab initio F and F^2 terms to the original lagrangian we render the
model renormalizable. We determine the renormalization constants and beta
functions through two loops, thus making it possible to study the
renormalization group flow of the nonanticommutation parameter.
