<p>This paper investigates the nonlinear dynamic behavior of an axially moving magnetostrictive rectangular plate subjected to air-gap fields and mechanical loads. Under the combined action of magnetic fields and mechanical loads, the magnetostrictive effect and its inverse effect are deeply coupled within the plate, leading to complex magneto-elastic coupling behavior. This results in a highly nonlinear constitutive relationship between the internal magnetic field intensity and strain of the plate. Based on the nonlinear magnetostrictive constitutive relations and considering the feedback effect of deflection on the magnetic field, a general analytical framework for the air-gap field is established. Building upon this foundation, the geometric large deformation, electromagnetic forces, and parametric excitation induced by time-varying speed are comprehensively incorporated to derive the nonlinear magneto-elastic coupling governing equations of the system. The method of multiple scales is applied to obtain analytical solutions, yielding the amplitude-frequency response equations under superharmonic-principal parametric combined resonance. The evolution of amplitude with multiple physical parameters is analyzed, and the accuracy of the analytical results is verified through numerical simulations. The results reveal that under parameter-excitation coupling conditions, the system exhibits strongly nonlinear characteristics, with its amplitude and distribution of steady-state solutions being regulated by multiple parameters. Notably, the nonlinear magneto-elastic coupling effect induces a dynamic transition between softening and hardening spring characteristics. The fundamental cause of the above complex dynamic phenomena lies in the nonlinear competition and evolution between the equivalent stiffness and multiple excitations, both modulated by system parameters.</p>