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Anterior chamber angle (ACA) classification is a key step in the diagnosis of angle-closure glaucoma in Anterior Segment Optical Coherence Tomography (AS-OCT). Existing automated analysis methods focus on a binary classification system (i.e., open angle or angle-closure) in a 2D AS-OCT slice. However, clinical diagnosis requires a more discriminating ACA three-class system (i.e., open, narrow, or synechiae angles) for the benefit of clinicians who seek better to understand the progression of the spectrum of angle-closure glaucoma types. To address this, we propose a novel sequence multi-scale aggregation deep network (SMA-Net) for open-narrow-synechiae ACA classification based on an AS-OCT sequence. In our method, a Multi-Scale Discriminative Aggregation (MSDA) block is utilized to learn the multi-scale representations at slice level, while a ConvLSTM is introduced to study the temporal dynamics of these representations at sequence level. Finally, a multi-level loss function is used to combine the slice-based and sequence-based losses. The proposed method is evaluated across two AS-OCT datasets. The experimental results show that the proposed method outperforms existing state-of-the-art methods in applicability, effectiveness, and accuracy. We believe this work to be the first attempt to classify ACAs into open, narrow, or synechia types grading using AS-OCT sequences.