Manifest supersymmetry in non-commutative geometry

We consider the open superstring ending on a D-brane in the presence of a c onstant NS-NS B field, using the Green-Schwarz formalism. Quantizing in the light-cone gauge, we find that the anti-commutation relations for the ferm ionic variables of superspace remain unmodified. We also derive the unbroke n supersymmetry algebra living on the D-brane. This establishes how the Moy al product is extended in a superspace formulation of non-commutative field theories. The superfield formulation of non-commutative supersymmetric fie ld theories is briefly considered.