In this study, to investigate the electromechanically coupled dynamics of a dual-motor electric drive system (DEDS) of hybrid electric vehicles under typical conditions. Considering the time-varying stiffness of gears, a dynamic model of the gear system and permanent magnet synchronous motor (PMSM) was developed, and a comprehensive electromechanical coupling dynamics model of DEDS applicable to coupling dynamics analysis was obtained. Based on this model, the impacts of the transmission error and electromechanical coupling effect on the dynamics of DEDS under steady-state and acceleration conditions were simulated and analyzed. This study demonstrates the significant impact of transmission errors on the dynamic load of high-speed gear pairs and the speed synchronization characteristics of the system. The study also reveals that the electromechanical coupling effect exacerbated the fluctuation of the gear dynamic load. During the speed change process, the electromechanical coupling effect did not introduce new resonance points. However, transmission errors tend to induce low-frequency resonance of the gear dynamic load and speed synchronization error (SSE). In addition, when the system is operated near the resonant speed, a large torsional vibration dominated by the resonant excitation frequency is generated, distinguished using the current signal to assess the resonance risk. The research results are important for the integrated design and condition monitoring of DEDS and offer valuable insights for enhancing the operational efficiency and reliability of the system.