Dynamic properties of ferromagnetic nematic liquid crystals under an external magnetic field have investigated. The coupled dynamics of the magnetization, M, and the director field, n, associated with the liquid crystalline orientation order, have studied. In the framework of the hydrodynamicand 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.