  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).
