AbstractIn this lecture we review some contributions to the study of dynamical questions inN= 2 supersymmetric string compactifications. The recurrent themes are the relation between perturbative heterotic couplings, expressed in terms of certain modular forms, and the corresponding type II couplings, determined by genusginstanton numbers. The investigation is performed concentrating on theN= 2 prepotential and on the gravitational couplingF1, for a particular heterotic/type II dual string pair. The relation to theN= 4 situation is also briefly discussed.