  We present a supersymmetric version of Dirac-Born-Infeld (DBI) theory in
noncommutative space-time, both for Abelian and non-Abelian gauge groups. We
show, using the superfield formalism, that the definition of a certain ordering
with respect to the * product leads naturally to a DBI action both in the U(1)
as well as in the U(N) case. BPS equations are analysed in this context and
properties of the resulting theory are discussed.
