The N = 2 fermionic extensions of the KdV equations are derived from the zero curvature condition associated with the graded Lie algebra of OSp(2/2). These equations lead to two bi-Hamiltonian systems one of which is supersymmetric. We also derive the one-parameter family of N = 2 supersymmetric KdV equation without a bi-Hamiltonian structure in this approach. Following our earlier proposal, we interpret the zero curvature condition as a gauge anomaly equation which brings our the underlying current algebra for the corresponding 2D-supergravity theory. This current algebra is, then, used to obtain the operator product expansions of various fields of this theory. (author). 34 refs.