Abstract: In the calculation of optimal energy flow of integrated electric-gas systems, the assumption of pipeline parameter homogenization makes it difficult for physical models to accurately describe the dynamic process of gas network. Therefore, this paper proposes a calculation model for the optimal energy flow of the integrated electric-gas systems based on the dynamic surrogate model of the gas network. Based on neural network fitting the relationship between gas network flow and pressure, the neural network parameters are extracted to build the dynamic surrogate model of gas network. The construction method of rolling surrogate model based on the maximum time constant of gas network is proposed. The gas network dynamic surrogate model with nonlinear activation function is equivalent to the mixed integer linear programming model, and can be combined with the power system power flow model to establish the optimal energy flow model of the integrated electric-gas systems. The model proposed in this paper is verified and analyzed in the distribution network level integrated electric-gas systems. The results show that the proposed method has high accuracy compared with the physical model based on the assumption of pipeline parameter homogenization and the gas network full time surrogate model, reducing the surrogate model size and the model training cost.