  We consider nonanticommutative SYM theories with chiral matter in the adjoint
representation of the SU(N) x U(1) gauge group. In a superspace setup and
manifest background covariant approach we investigate the one-loop
renormalization of the theory when a cubic superpotential is present. The
structure of the divergent terms reveals that the theory simply obtained from
the ordinary one by trading products for star products is not renormalizable.
Moreover, because of the different renormalization undergone by the abelian
field compared to the non-abelian ones, the superpotential seems to be
incompatible with the requests of renormalizability, gauge and N=1/2
invariance. However, by a suitable modification of the quadratic action for the
U(1) (anti)chiral superfields and the addition of extra couplings, we find an
action which is one-loop renormalizable and manifestly N=1/2 supersymmetric and
supergauge invariant. We conclude that interacting matter can be safely
introduced in NAC gauge theories, in contrast with previous results.
