  We study the non-perturbative properties of N=2 super conformal field
theories in four dimensions using localization techniques. In particular we
consider SU(2) gauge theories, deformed by a generic epsilon-background, with
four fundamental flavors or with one adjoint hypermultiplet. In both cases we
explicitly compute the first few instanton corrections to the partition
function and the prepotential using Nekrasov's approach. These results allow to
reconstruct exact expressions involving quasi-modular functions of the bare
gauge coupling constant and to show that the prepotential terms satisfy a
modular anomaly equation that takes the form of a recursion relation with an
explicitly epsilon-dependent term. We then investigate the implications of this
recursion relation on the modular properties of the effective theory and find
that with a suitable redefinition of the prepotential and of the effective
coupling it is possible, at least up to the third order in the deformation
parameters, to cast the S-duality relations in the same form as they appear in
the Seiberg-Witten solution of the undeformed theory.
