A generalization of the force-free equation describing steady-state axially symmetric flows in the vicinity of a Kerr black hole is carried out to the case of ideal magnetohydrodynamics. It is shown how this equation changes from an elliptic to a hyperbolic type in the vicinity of the horizon. The limits of applicability of the approach under discussion are examined for different astrophysical sources. It is shown that a high photon density strongly restricts the limits of applicability of the MHD approach.