We propose a novel framework for multi-person 3D motion trajectoryprediction. Our key observation is that a human's action and behaviors mayhighly depend on the other persons around. Thus, instead of predicting eachhuman pose trajectory in isolation, we introduce a Multi-Range Transformersmodel which contains of a local-range encoder for individual motion and aglobal-range encoder for social interactions. The Transformer decoder thenperforms prediction for each person by taking a corresponding pose as a querywhich attends to both local and global-range encoder features. Our model notonly outperforms state-of-the-art methods on long-term 3D motion prediction,but also generates diverse social interactions. More interestingly, our modelcan even predict 15-person motion simultaneously by automatically dividing thepersons into different interaction groups. Project page with code is availableat https://jiashunwang.github.io/MRT/.