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Deepfakes are AI-synthesized multimedia data that may be abused for spreading misinformation. Deepfake generation involves both visual and audio manipulation. To detect audio-visual deepfakes, previous studies commonly employ two relatively independent sub-models to learn audio and visual features, respectively, and fuse them subsequently for deepfake detection. However, this may underutilize the inherent correlations between audio and visual features. Moreover, utilizing two isolated feature learning sub-models can result in redundant neural layers, making the overall model inefficient and impractical for resource-constrained environments. In this work, we design a lightweight network for audio-visual deepfake detection via a single-stream multi-modal learning framework. Specifically, we introduce a collaborative audio-visual learning block to efficiently integrate multi-modal information while learning the visual and audio features. By iteratively employing this block, our single-stream network achieves a continuous fusion of multi-modal features across its layers. Thus, our network efficiently captures visual and audio features without the need for excessive block stacking, resulting in a lightweight network design. Furthermore, we propose a multi-modal classification module that can boost the dependence of the visual and audio classifiers on modality content. It also enhances the whole resistance of the video classifier against the mismatches between audio and visual modalities. We conduct experiments on the DF-TIMIT, FakeAVCeleb, and DFDC benchmark datasets. Compared to state-of-the-art audio-visual joint detection methods, our method is significantly lightweight with only 0.48M parameters, yet it achieves superiority in both uni-modal and multi-modal deepfakes, as well as in unseen types of deepfakes.