<p>To address the challenges posed by the intricate coupling among various entities within an Integrated Energy System (IES), the competition for market position, the advantages of technological innovation, and the increased penetration of intermittent renewable energy sources (RES), this paper proposes a dual-Stackelberg game two-stage robust framework for optimization scheduling in IES. Firstly, through the coordinated operation of combined heat and power with carbon capture system and power-to-gas (CHP-CCS-P2G) and concentrated solar power with thermal energy storage (CSP-TES), the interconnection between electrical and thermal energy within the system is strengthened, and the carbon emissions of the Integrated Energy System (IES) are significantly reduced. Secondly, a dual-Stackelberg game model is formulated using game theory to accurately characterize the interaction dynamics among the distribution system operator (DSO), multi-energy flow microgrid (MEMG), and users. On this basis, by fully accounting for the uncertainty of renewable energy, a two-stage robust optimization model for the output of renewable energy in the MEMG is established. By integrating this model with the dual-Stackelberg game, a dual-Stackelberg game two-stage robust framework for optimization scheduling in IES is proposed. Furthermore, the Karush–Kuhn–Tucker (KKT) conditions are utilized to equivalently transform the MEMG and user two-layer model into an MGA single-layer model. The golden section search-based distribution method of embedded column and constraint generation (C&amp;CG) algorithm is employed to solve the Stackelberg game between the uncertain MGA and the DSO. Finally, the effectiveness of the proposed method is validated through numerical examples.</p>