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Accurate modeling of car-following behaviors is essential for various applications in traffic management and autonomous driving systems. However, current approaches often suffer from limitations like high sensitivity to data quality and lack of interpretability. In this study, we propose GenFollower, a novel zero-shot prompting approach that leverages large language models (LLMs) to address these challenges. We reframe car-following behavior as a language modeling problem and integrate heterogeneous inputs into structured prompts for LLMs. This approach achieves improved prediction performance and interpretability compared to traditional baseline models. Experiments on the Waymo Open datasets demonstrate GenFollower's superior performance and ability to provide interpretable insights into factors influencing car-following behavior. This work contributes to advancing the understanding and prediction of car-following behaviors, paving the way for enhanced traffic management and autonomous driving systems.