  In this paper we study the extension of Morita equivalence of noncommutative
tori to the supersymmetric case. The structure of the symmetry group yielding
Morita equivalence appears to be intact but its parameter field becomes
supersymmetrized having both body and soul parts. Our result is mainly in the
two dimensional case in which noncommutative supertori have been constructed
recently: The group $SO(2,2,V_{\Z}^0)$, where $V_{\Z}^0$ denotes Grassmann even
number whose body part belongs to ${\Z}$, yields Morita equivalent
noncommutative supertori in two dimensions.
