  We discuss the modular anomaly equation satisfied by the the prepotential of
4-dimensional N=2* theories and show that its validity is related to S-duality.
The recursion relations that follow from the modular anomaly equation allow one
to write the prepotential in terms of (quasi)-modular forms, thus resumming the
instanton contributions. These results can be checked against the microscopic
multi-instanton calculus in the case of classical algebras, but are valid also
for the exceptional E6, E7, E8, F4 and G2 algebras, where direct computations
are not available.
