  We study four dimensional supersymmetric gauge theory on the noncommutative
superspace, recently proposed by Seiberg. We construct the gauge-invariant
action of N=1 super Yang-Mills theory with chiral and antichiral superfields,
which has N=1/2 supersymmetry on the noncommutative superspace. We also
construct the action of N=2 super Yang-Mills theory. It is shown that this
theory has only N=1/2 supersymmetry.
