<p>This study aims to develop a visco-hyperelastic damage model for bilayer hard-magnetic elastomer membranes (HMEMs). A visco-hyperelastic damage model is proposed to analyze the viscoelastic deformations and damage behaviors of a bilayer HMEM under the coupled effect of an applied magnetic field and pressure. A set of governing equations is derived within the framework of finite deformation theory and hard-magnetic theory. The shooting method and the improved Euler method are employed to solve the equations. Numerical results are obtained by varying key parameters: the magnitude and orientation of remnant magnetization in each layer, pressure, applied magnetic field strength and direction, as well as the loading/unloading paths of both magnetic field and pressure. The entire deformation process includes three stages: inflation, creep, and unloading. Theoretical results display the large deformations of the bilayer HMEM during the inflation and creep stages. Distinct time-dependent unloading paths are applied for both the pressure and magnetic fields, leading to time-dependent mechanical responses. The presented model of bilayer HMEMs offers valuable insights for potential applications of hard-magnetic soft membrane-type actuators and structures.</p>