  We study the duality of the supersymmetric self-dual and Maxwell-Chern-Simons
theories coupled to a fermionic matter superfield, using a master action. This
approach evades the difficulties inherent to the quartic couplings that appear
when matter is represented by a scalar superfield. The price is that the
spinorial matter superfield represents a unusual supersymmetric multiplet,
whose main physical properties we also discuss.
