BPS Spectra and Non--Perturbative Couplings in N=2,4 Supersymmetric String Theories

We study the BPS spectrum in $D=4, N=4$ heterotic string compactifications, with some emphasis on intermediate $N=4$ BPS states. These intermediate states, which can become short in $N=2$ compactifications, are crucial for establishing an $S-T$ exchange symmetry in $N=2$ compactifications. We discuss the implications of a possible $S-T$ exchange symmetry for the $N=2$ BPS spectrum. Then we present the exact result for the 1-loop corrections to gravitational couplings in one of the heterotic $N=2$ models recently discussed by Harvey and Moore. We conjecture this model to have an $S-T$ exchange symmetry. This exchange symmetry can then be used to evaluate non-perturbative corrections to gravitational couplings in some of the non-perturbative regions (chambers) in this particular model and also in other heterotic models.