Dynamic properties of ferromagnetic nematic liquid crystals under an external magnetic field have investigated. The coupled dynamics of the magnetization,, and the director field, , associated with the liquid crystalline orientation order, have studied. In the framework of the hydrodynamic and and thermodynamic approach, the role of the dynamic cross-coupling in macroscopic dynamic behavior both the nematic liquid crystal and its magneto-optic properties is considered. The dependence of the temporal evolution of a magneto-induced response on the dissipative and reversible parts of the dynamic cross-coupling is considered.