Abstract: The goal of efficient and low-carbon energy utilization has led to a close coupling between the electric and gas system, forming an integrated energy system (IES) consisting of energy production, distribution and consumption in the region. In order to clarify the interaction between the subsystems and to improve the control of IES, relevant researches have gradually extended from the steady-state analysis to the dynamic analysis. However, the significant differences in dynamic characteristics, time constants, and modelling methods of different subsystems pose great challenges to the dynamic process simulation and control strategy verification of IES. To effectively reveal the coupling mechanism of dynamic processes in electric and gas network operation, this paper foucused on the electric-gas IES with two-way energy coupling. Firstly, on the basis of steady-state power flow calculation, the characteristic line method was used to realize the numerical solution of the dynamic process for the natural gas network. Then, dynamic models of the two-way coupling were established, and a complete dynamic multi-rate co-simulation method was proposed for the electric-gas IES. Finally, two typical scenarios reflecting dynamic process of two-way electric-gas coupling system were used for simulation verification, The results show that the model and algorithm can effectively reflect the interaction between gas and electric systems in different dynamic processes, providing a favorable means for the study of dynamic processes of IES.