On space-time supersymmetry and string duality in nine dimensions

N = 2 extended space-time supersymmetry in nine dimensions implies that the BPS states corresponding to momentum and winding of either of the type-II superstrings compactified on S-1 transform as inequivalent supermultiplets. This fact can be checked using world-sheet techniques, and provides the ph ysical basis for the connection between IIA superstring theory compactified on a circle of radius R and IIB theory compactified on a circle of radius 1/R. Aspects of the duality between hi-theory compactified on T-2 and IIB t heory compactified on S' follow from the structure of N = 2, D = 9 supergra vity. The coupling of N = 2, D = 9 supergravity to the BPS states is also d iscussed.