  We discuss R-symmetries in locally supersymmetric N=2 gauge theories coupled
to hypermultiplets which can be thought of as effective theories of heterotic
superstring models. In this type of supergravities a suitable R-symmetry exists
and can be used to topologically twist the theory: the vector multiplet
containing the dilaton-axion field has different R-charge assignments with
respect to the other vector multiplets. Correspondingly a system of coupled
instanton equations emerges, mixing gravitational and Yang--Mills instantons
with triholomorphic hyperinstantons and axion-instantons. For the tree-level
classical special manifolds $ST(n)=SU(1,1)/U(1)\times SO(2,n)/(SO(2)$ $\times
SO(n))$ R-symmetry with the specified properties is a continuous symmetry, but
for the quantum corrected manifolds ${\hat {ST}}(n)$ a discrete R--group of
electric--magnetic duality rotations is sufficient and we argue that it exists.
