  An explicitly exact superconformal description is provided to some classes of
Type II string theories in non constant RR backgrounds. This is done by
applying the manifest (2,2) approach of Berkovits and Maldacena to Type II
strings and by studying the condition of exact conformal invariance of certain
supersymmetric backgrounds. We find a new set of exact type IIA strings with
non constant RR 2-form and 4-form curvatures and for type IIB with non constant
3-form curvature.
