We consider duality transformations in N = 2, d = 4 Yang-Mills theory coupled to N = 2 supergravity. A symplectic and coordinate covariant framework is established, which allows one to discuss stringy ''classical and quantum duality symmetries'' (monodromies), incorporating T-and S-dualities. In particular, we shall be able to study theories (like N = 2 heterotic strings) which are formulated in symplectic basis where a ''holomorphic prepotential'' F does not exist, and yet give general expressions for all relevant physical quantities. Duality transformations and symmetries for the N = 1 matter coupled Yang-Mills supergravity system are also exhibited. The implications of duality symmetry on all N > 2 extended supergravities are briefly mentioned. We finally give the general form of the central charge and the N = 2 semiclassical spectrum of the dyonic BPS saturated states (as it comes by truncation of the N = 4 spectrum).