T-duality Covariance of SuperD-branes

T-duality realized on SuperD-brane effective actions probing in constant $G_{mn}$ and $b_{mn}$ backgrounds is studied from a pure world volume point of view. It is proved that requiring {\em T-duality covariance} of such actions ``fixes'' the T-duality transformations of the world volume dynamical fields, and consequently, of the NS-NS and R-R coupling superfields. The analysis is extended to uncover the mapping of the symmetry structure associated with these SuperD-brane actions. In particular, we determine the T-duality transformation properties of kappa symmetry and supersymmetry, which allow us to prove that bosonic supersymmetric world volume solitons of the original theory generate, through T-duality, the expected ones in the T-dual theory. The latter proof is generalized to arbitrary bosonic backgrounds. We conclude with some comments on extensions of our approach to arbitrary kappa symmetric backgrounds, non-BPS D-branes and non-abelian SuperD-branes.