  First we consider the deformations of superspaces with N=(1,1) and N=(2,2)
supersymmetries in two dimensions. Among these the construction of
noncommutative supertorus with odd spin structure is possible only in the case
of N=(2,2) supersymmetry broken down to N=(1,1). However, for the even spin
structures the construction of noncommutative supertorus is possible for both
N=(1,1) and N=(2,2) cases. The spin structures are realized by implementing the
translational properties along the cycles of commutative supertorus in the
operator version: Odd spin structure is realized by the translation in the
fermionic direction in the same manner as in the construction of noncommutative
torus, and even spin structures are realized with appropriate versions of the
spin angular momentum operator.
