  Kerr black hole immersed in test, asymptotically homogeneous magnetic field,
aligned along the symmetry axis, is described by Wald's solution. We show how
the static case of this solution may be generalized for nonlinear
electromagnetic models via perturbative approach. Using this technique we find
the lowest order correction to Wald's solution on Schwarzschild spacetime in
Euler--Heisenberg and Born--Infeld theories. Finally, we discuss the problem of
highly conducting star in asymptotically homogeneous magnetic field.
