  In this paper, we discuss the generalizations of exact supersymmetries
present in the supersymmetrized sigma models. These generalizations are made by
making the supersymmetric transformation parameter field-dependent. Remarkably,
the supersymmetric effective actions emerge naturally through the Jacobian
associated with the generalized supersymmetry transformations. We explicitly
demonstrate these for two different supersymmetric sigma models, namely, one
dimensional sigma model and topological sigma model for hyperinstantons on
quaternionic manifold.
