We report a theoretical formalism that describes a dynamic magnetic response of rare-earth orthoferrites, particularly those with non-Kramers rare-earth () ions, when driven by strong terahertz fields. We derive a total thermodynamic potential for the exchange coupled -Fe system by constructing an effective Hamiltonian and employing a mean-field theory approximation. We investigate static properties of the and Fe subsystems across the spin-reorientation phase transitions and obtain resonance frequencies for Fe and magnetic sublattices as a function of temperature. Taking an example of the archetypical orthoferrite TmFeO3, we perform numerical modeling to accurately describe the behavior of its anisotropy functions vs temperature. Finally, we analyze switching dynamics of Fe spins and nonlinear effects in the subsystem of TmFeO3 driven by strong terahertz radiation. Published by the American Physical Society 2025