  The background field method for N=2 super Yang-Mills theories in harmonic
superspace is developed. The ghost structure of the theory is investigated. It
is shown that the ghosts include two fermionic real omega-hypermultiplets
(Faddeev-Popov ghosts) and one bosonic real omega-hypermultiplet
(Nielsen-Kallosh ghost), all in the adjoint representation of the gauge group.
The one-loop effective action is analysed in detail and it is found that its
structure is determined only by the ghost corrections in the pure super
Yang-Mills theory. As applied to the case of N=4 super Yang-Mills theory,
realized in terms of N=2 superfields, the latter result leads to the remarkable
conclusion that the one-loop effective action of the theory does not contain
quantum corrections depending on the N=2 gauge superfield only. We show that
the leading low-energy contribution to the one-loop effective action in the N=2
SU(2) super Yang-Mills theory coincides with Seiberg's perturbative holomorphic
effective action.
