In recent years, researchers combine both audio and video signals to deal with challenges where actions are not well represented or captured by visual cues. However, how to effectively leverage the two modalities is still under development. In this work, we develop a multiscale multimodal Transformer (MMT) that leverages hierarchical representation learning. Particularly, MMT is composed of a novel multiscale audio Transformer (MAT) and a multiscale video Transformer [43]. To learn a discriminative cross-modality fusion, we further design multimodal supervised contrastive objectives called audio-video contrastive loss (AVC) and intra-modal contrastive loss (IMC) that robustly align the two modalities. MMT surpasses previous state-of-the-art approaches by 7.3% and 2.1% on Kinetics-Sounds and VGGSound in terms of the top-1 accuracy without external training data. Moreover, the proposed MAT significantly outperforms AST [28] by 22.2%, 4.4% and 4.7% on three public benchmark datasets, and is about 3% more efficient based on the number of FLOPs and 9.8% more efficient based on GPU memory usage.