  Self-duality equations for Yang-Mills fields in d-dimensional Euclidean
spaces consist of linear algebraic relations amongst the components of the
curvature tensor which imply the Yang-Mills equations. For the extension to
superspace gauge fields, the super self-duality equations are investigated,
namely, systems of linear algebraic relations on the components of the
supercurvature, which imply the self-duality equations on the even part of
superspace. A group theory based algorithm for finding such systems is
developed. Representative examples in various dimensions are provided,
including the Spin(7) and G(2) invariant systems in d=8 and 7, respectively.
