The deep integration of electricity and carbon markets introduces new challenges for trading behavior modeling, driven by strategic diversity, adaptive agent behaviors, and bidirectional market feedback. Traditional optimization and game-theoretic formulations, which rely on fixed rationality assumptions and static behavioral structures, often fail to capture these dynamics with sufficient fidelity. This paper proposes a large language model (LLM)-augmented multi-agent system (MAS) framework for trading behavior modeling in coupled electricity- carbon markets, where LLMs act as cognitive agents capable of generating context-dependent strategies, interpreting market rules, and responding to evolving system states. The MAS provides a structured environment for interaction among heterogeneous agents, enabling more expressive, adaptive, and interpretable representations of cross-market behaviors. Case studies based on China’ s coupled electricity- carbon markets demonstrate that the proposed framework can reflect realistic bidding responses, emission-driven adjustments, and market feedback dynamics. This paper also identifies key challenges and outlines future directions including constraint-aware generation to ensure feasibility, structured reasoning and memory to enhance interpretability, and improved computational efficiency to enable scalable MAS deployment.