A Note on Superdistributions and Wavefront Set

We present a simple and new method of constructing superdistributions on superspace over a Grassmann-Banach algebra, which close to the de Rham's ``currents'' defined as dual objects to differential forms. The paper also contains the extension of the H\"ormander's description of the singularity structure (wavefront set) of a distribution to include the supersymmetric case.