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To facilitate the coupling of electricity and carbon markets, a two-layer bidding model considering a multi-stage offer‑carbon joint incentive clearing mechanism is proposed. The upper layer models the bidding strategies of renewable energy units and thermal power generating units, and the lower layer is the market clearing layer. A multi-stage offer‑carbon joint incentive clearing mechanism is proposed. In the pre-clearing stage, the environmental benefit factor of the carbon market is introduced to adjust the bidding strategy of the units, the carbon emission intensity enters the market in the form of price, the environmental benefit of the generating units is fully considered, and the carbon quota allocation model of units is established; in the second stage, carbon trading cost is added based on the pre-clearing model to further optimize the unit output; in the third stage, the clearing model with the minimum cost of electricity energy is established for tracking the clearing price. Under this mechanism, the carbon trading cost is traded on the market and unit offers are combined with carbon element to participate in market trading. Three bidding models with different clearing mechanisms are set up, and the results of the arithmetic example show that the proposed model can realize the balance between the economic and low-carbon goals of market clearing, and can achieve the maximum carbon emission reduction based on no increase in the total cost of electric-carbon coupling. As the share of renewable energy increases, the clearing price will decrease. A reasonable offer from renewable energy sources can avoid their interests being jeopardized. Concurrently, increasing the initial carbon price can effectively guide the electricity market to develop in a cleaner direction. • Pre-clearing phase is introduced to adjust bidding strategies. • A multi-stage offer-carbon joint incentive clearing mechanism is proposed. • A two-layer bidding model considering a multi-stage offer-carbon joint incentive clearing mechanism. • The market equilibrium problem is modeled as a two-layer problem, and the model is solved by Aquila Optimizer. [ABSTRACT FROM AUTHOR]