  We find exact charged black hole solutions of a string effective action that
is invariant under S-duality transformations. These black hole solutions have
the same causal structure as the Reissner-Nordstrom (RN) solutions. They reduce
to the RN solutions for self-dual configurations of the dilaton and to the
Garfinkle-Horowitz-Strominger (GHS) solution in the weak (or strong) coupling
regime. Using the purely magnetic solutions of the S-duality model we also
generate dyonic black hole solutions of the GHS model, which have the causal
structure of the RN solutions.
