Abstract: With the development of integrated energy system and the promotion of its marketization operation, it is of great significance to study the equilibrium strategy of demand response for integrated energy service providers in the multi-energy market environment. Firstly, a bi-level decision model of integrated energy service providers interacting with the electricity and gas markets is developed, where the upper problem describes the games of power generators and gas companies competing in the electricity and gas markets respectively by bidding as a supply function. The lower problem describes the integrated demand response behavior of integrated energy service providers making decisions on electricity and gas purchasing, electricity and heat consuming and gas dispatching according to the market prices for electricity and gas. In order to solve the bi-level model, the solution of the upper problem is transformed into the solution of the ordinal potential function of the electricity and gas markets respectively, and the solution of the lower problem is transformed into the solution of the exact potential function, and the uniqueness of the solution for the bi-level model is theoretically proved. Considering the incompleteness of information in practical application, the distributed algorithm is used to solve the bi-level model. Finally, the simulation results show that the use of integrated demand response can reduce price differences in the electricity and gas markets, increase the demand-side profits, add the social welfare, and raise the average electricity utility coefficient and average gas-to-electricity efficiency, both of which will promote the social welfare.