Previous stance detection studies typically concentrate on evaluating stances within individual instances, thereby exhibiting limitations in effectively modeling multi-party discussions concerning the same specific topic, as naturally transpire in authentic social media interactions. This constraint arises primarily due to the scarcity of datasets that authentically replicate real social media contexts, hindering the research progress of conversational stance detection. In this paper, we introduce a new multi-turn conversation stance detection dataset (called \textbf{MT-CSD}), which encompasses multiple targets for conversational stance detection. To derive stances from this challenging dataset, we propose a global-local attention network (\textbf{GLAN}) to address both long and short-range dependencies inherent in conversational data. Notably, even state-of-the-art stance detection methods, exemplified by GLAN, exhibit an accuracy of only 50.47\%, highlighting the persistent challenges in conversational stance detection. Furthermore, our MT-CSD dataset serves as a valuable resource to catalyze advancements in cross-domain stance detection, where a classifier is adapted from a different yet related target. We believe that MT-CSD will contribute to advancing real-world applications of stance detection research. Our source code, data, and models are available at \url{https://github.com/nfq729/MT-CSD}.

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