Electromechanical integrating toroidal drive is a new-style generalized composite transmission, in which drive, power and control are integrated. Nonlinear electromagnetic meshing force can lead to obvious internal resonance during operation and cause drive system to run unusually. In this paper, for the nonlinear electromagnetic mesh forces between planets, worm and stator, strongly nonlinear dynamic differential equations of toroidal drive are presented. Based on two different situations of internal resonance and non-internal resonance, the first order approximate analytic solutions of time responses are obtained by multiscale method. Time responses of vibration amplitudes and displacements of the drive system are obtained. Meanwhile, changes of time responses of the different components for the drive system under the two situations of the internal resonance and non-internal resonance are investigated. The results show that the internal resonance makes energy alternately transfer between different components. It leads to increase of amplitudes and affects dynamic performance of drive system, so it should be removed during design.