TYPE IIA IIB STRING DUALITY FOR TARGETS WITH ABELIAN ISOMETRIES/

We examine T-duality transformations for supersymmetric strings with t arget space geometry with compact abelian isometries. We consider the partition function of these models and we show that although T-duality is not a symmetry, due to an anomaly, it relates type IIA to type IIB strings. In this way we extend the corresponding result for toroidal compactification to the general case of non-trivial backgrounds with a belian isometries and for world sheets of any genera.