The existence of multiple-source nonlinear excitation inside the electric vehicle integrated electric drive system (IEDS) makes the localization of vibration sources and vibration suppression more complicated. To study the dynamic characteristics of the IEDS of pure electric vehicles during operation, a multiple-domain coupling dynamics model of the IEDS for steady/transient state is proposed based on the equivalent magnetic network and the finite unit method, taking into consideration of the permanent magnet synchronous motor and gear system body structure, nonlinear magnetic field factors, shaft flexibility and time-varying meshing stiffness and others. The coupling mechanism and vibration characteristics of the IEDS under accelerated and suddenly changing load conditions are investigated by means of dynamic analysis. The results of the study show that the internal excitation of the IEDS under acceleration conditions is prone to resonance phenomena. In the resonance speed, will occur in the resonance frequency as the dominant violent vibration, the current spectrum by the modulation of the meshing frequency will show obvious frequency domain characteristics, can be through the current low-frequency signal to monitor the resonance of the gear system. Under abrupt load excitation, the systems all exhibit transient free vibration dominated by the first-order intrinsic frequency, which gradually diminishes under the influence of structural damping. A modulation effect occurs in the frequency domain of the motor current, which can be expressed as |fe ± fN1|. The coupling effect of the IEDS effectively suppresses shock oscillations caused by sudden changes in external loads.