  We consider noncommutative analogs of scalar electrodynamics and N=2 D=4 SUSY
Yang-Mills theory. We show that one-loop renormalizability of noncommutative
scalar electrodynamics requires the scalar potential to be an anticommutator
squared. This form of the scalar potential differs from the one expected from
the point of view of noncommutative gauge theories with extended SUSY
containing a square of commutator. We show that fermion contributions restore
the commutator in the scalar potential. This provides one-loop
renormalizability of noncommutative N=2 SUSY gauge theory. We demonstrate a
presence of non-integrable IR singularities in noncommutative scalar
electrodynamics for general coupling constants. We find that for a special
ratio of coupling constants these IR singularities vanish. Also we show that IR
poles are absent in noncommutative N=2 SUSY gauge theory.
