In order to promote cleanable energy consumption, this paper proposes a multi-energy system operation control strategy. Considering the participation of multi-energy system in the day-ahead power market, the real-time power market, and the gas market, a two-stage robust stochastic optimization model is proposed with the objective of minimizing the total system operating cost, using dualization to deal with the price uncertainty in the day-ahead market, and Monte Carlo methods to deal with other uncertain parameters. In order to satisfy the dynamic power balance constraints in the day-ahead market, an interaction management mechanism is used to deal with the power imbalance among multi-energy subsystems. Furthermore, auxiliary services based on demand response and direct load control are provided to increase operational revenues. The feasibility of the proposed approach is verified through a set of case studies. Simulation results show that the total operating cost of the multi-energy system is reduced by at least 9% considering multiple-economic coordination, which validates the effectiveness of the proposed method.