  We study the possibility of establishing the dual equivalence between the
noncommutative Maxwell-Chern-Simons theory and the noncommutative self-dual
theory. It turns to be that whereas in the commutative case the
Maxwell-Chern-Simons theory can be mapped into the sum of the self-dual theory
and the Chern-Simons theory, in the noncommutative case such a mapping is
possible only for the theory with the modified Maxwell term.
