  We review a recent progress in constructing 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(1)^(n-1).
General structure of leading low-energy corrections to effective action is
discussed.
