In an integrated energy system, the growing number of distributed heat and electric power generation units will bring new technical challenges to the existing centralized economic dispatch strategies. This paper proposes a distributed optimization approach for the economic system operation in a multienergy system by considering various equality and inequality constraints to accommodate the integration of intermittent renewable generations. The proposed distributed neurodynamic-based approach only requires the information exchange among neighboring units and offers flexibility, adaptivity, scalability, faster convergence, and lower communication burden compared with some traditional centralized methods. The simulation results of two integrated energy systems validate the effectiveness of the proposed distributed approach. Comparisons with other centralized and distributed optimization methods quantify the advantages of the proposed distributed approach in terms of convergence speed and computation complexity.