  We derive a modular anomaly equation satisfied by the prepotential of the
N=2* supersymmetric theories with non-simply laced gauge algebras, including
the classical B and C infinite series and the exceptional F4 and G2 cases. This
equation determines the exact prepotential recursively in an expansion for
small mass in terms of quasi-modular forms of the S-duality group. We also
discuss the behaviour of these theories under S-duality and show that the
prepotential of the SO(2r+1) theory is mapped to that of the Sp(2r) theory and
viceversa, while the exceptional F4 and G2 theories are mapped into themselves
(up to a rotation of the roots) in analogy with what happens for the N=4
supersymmetric theories. These results extend the analysis for the simply laced
groups presented in a companion paper.
