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We present a B\"acklund transformation (a discrete symmetry transformation)for the self-duality equations for supersymmetric gauge theories in N-extendedsuper-Minkowski space ${\cal M}^{4|4N}$ for an arbitrary semisimple gaugegroup. For the case of an $A_1$ gauge algebra we integrate the transformationstarting with a given solution and iterating the process we construct ahierarchy of explicit solutions.Comment: 10 pages, plaintex, IHEP 92-17

Bäcklund Transformation for Supersymmetric Self-Dual Theories for Semisimple Gauge Groups and a Hierarchy of Ai Solutions