  We obtain the T-duality transformations of space-time spinors (the
supersymmetry transformation parameters, gravitinos and dilatinos) of type-II
theories in curved backgrounds with an isometry. The transformation of the
spinor index is shown to be a consequence of the twist that T-duality
introduces between the left and right-moving local Lorentz frames. The result
is then used to derive the T-duality action on Ramond-Ramond field strengths
and potentials in a simple way. We also discuss the massive IIA theory and,
using duality, give a short derivation of ``mass''-dependent terms in the
Wess-Zumino actions on the D-brane worldvolumes.
