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Starting from the known representation of the Kac-Moody algebra in terms ofthe coordinates and momenta, we extend it to the representation of the superKac-Moody and super Virasoro algebras. Then we use general canonical method toconstruct an action invariant under local gauge symmetries, where components ofthe super energy-momentum tensor $L_\pm$ and $G_\pm$ play the role of thediffeomorphisms and supersymmetries generators respectively. We obtaincovariant extension of WZNW theory with respect to local supersymmetry as wellas explicit expressions for gauge transformations.Comment: LaTeX, 13 page

CANONICAL APPROACH TO 2D SUPERSYMMETRIC WZNW MODEL COUPLED TO SUPERGRAVITY