  We present a systematic investigation of one-loop renormalizability for
nonanticommutative N=1/2, U(N) SYM theory in superspace. We first discuss
classical gauge invariance of the pure gauge theory and show that in
contradistinction to the ordinary anticommutative case, different
representations of supercovariant derivatives and field strengths do not lead
to equivalent descriptions of the theory. Subsequently we develop background
field methods which allow us to compute a manifestly covariant gauge effective
action. One-loop evaluation of divergent contributions reveals that the theory
simply obtained from the ordinary one by trading products for star products is
not renormalizable. In the case of SYM with no matter we present a N=1/2
improved action which we show to be one-loop renormalizable and which is
perfectly compatible with the algebraic structure of the star product. For this
action we compute the beta functions. A brief discussion on the inclusion of
chiral matter is also presented.
