  We study a problem of low-energy effective action in N=4 super Yang-Mills
theories. Using harmonic superspace approach we consider N=4 SYM in terms of
unconstrained N=2 superfield and apply N=2 background field method to finding
effective action for N=4 SU(n) SYM broken down to U(n)$^{n-1}$. General
structure of leading low-energy corrections to effective action is discussed
and calculational procedure for their explicit finding is presented.
