Abstract: Sequential recommendation and group recommendation are two important branches in the field of recommender system. While considerable efforts have been devoted to these two branches in an independent way, we combine them by proposing the novel sequential group recommendation problem which enables modeling group dynamic representations and is crucial for achieving better group recommendation performance. The major challenge of the problem is how to effectively learn dynamic group representations based on the sequential user-item interactions of group members in the past time frames. To address this, we devise a Group-aware Long- and Short-term Graph Representation Learning approach, namely GLS-GRL, for sequential group recommendation. Specifically, for a target group, we construct a group-aware long-term graph to capture user-item interactions and item-item co-occurrence in the whole history, and a group-aware short-term graph to contain the same information regarding only the current time frame. Based on the graphs, GLS-GRL performs graph representation learning to obtain long-term and short-term user representations, and further adaptively fuse them to gain integrated user representations. Finally, group representations are obtained by a constrained user-interacted attention mechanism which encodes the correlations between group members. Comprehensive experiments demonstrate that GLS-GRL achieves better performance than several strong alternatives coming from sequential recommendation and group recommendation methods, validating the effectiveness of the core components in GLS-GRL.