The holomorphic effective action in N=2 D=4 supergauge theories with various gauge groups

We consider the theory of hypermultiplets in arbitary representations of ar bitrary semisimple gauge groups coupled to gauge superfields. Using the N = 2 harmonic superspace formulation of these models, we find the general str ucture of the holomorphic effective action depending on the gauge superfiel d with values in the Cartan subalgebra of the gauge algebra. We find explic it expressions for the effective actions in the cases where the hypermultip lets are in the fundamental and adjoint representations of SU(n), SO(n), an d Sp(2n).