  We examine T-duality transformations for supersymmetric strings with target
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 abelian isometries and for world sheets of
any genera.
