We present a supersymmetric version of Dirac-Born-Infeld (DBI) theory in no
ncommutative space-time, both for Abelian and non-Abelian gauge groups. We
show, using the superfield formalism, that the definition of a certain orde
ring with respect to the * product lends naturally to a DBI action both in
the U(I) as well as in the U(N) case. BPS equations are analysed in this co
ntext and properties of the resulting theory are discussed. (C) 2000 Elsevi
er Science B.V. All rights reserved.