  We consider N=4 supersymmetric Yang-Mills theory formulated in terms of N=2
superfields in harmonic superspace. Using the background field method we define
manifestly gauge invariant and N=2 supersymmetric effective action depending on
N=2 strength superfields and develop a general procedure for its calculation in
one-loop approximation. Explicit form for this effective action is found for
the case of SU(2) gauge group broken down to U(1).
