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Nonlinear differential equations for an electromechanical integrated magnetic gear (EIMG) system are developed by considering the nonlinearity in the magnetic force of the system components. Expressions for the main resonances and superharmonic resonances are obtained for output wave frequencies close to the natural frequency and half the natural frequency of the derived EIMG system. The response laws are discussed in detail. The magnetic coupling stiffness among the components is found to exhibit distinct nonlinearity, leading to strong main resonances and superharmonic resonances. Smaller values of the magnetic coupling stiffness and damping result in larger response amplitudes and transient responses that slowly decay to zero. When the main resonances and superharmonic resonances occur, the dominant frequency of the response is the natural frequency of the derived EIMG system, and the amplitudes of different components of the resonance display large differences.