Abstract: Accurate and timely air quality and weather predictions are of great importance to urban governance and human livelihood. Though many efforts have been made for air quality or weather prediction, most of them simply employ one another as feature input, which ignores the inner-connection between two predictive tasks. On the one hand, the accurate prediction of one task can help improve another task's performance. On the other hand, geospatially distributed air quality and weather monitoring stations provide additional hints for city-wide spatiotemporal dependency modeling. Inspired by the above two insights, in this paper, we propose the Multi-adversarial spatiotemporal recurrent Graph Neural Networks (MasterGNN) for joint air quality and weather prediction. Specifically, we first propose a heterogeneous recurrent graph neural network to model the spatiotemporal autocorrelation among air quality and weather monitoring stations. Then, we develop a multi-adversarial graph learning framework to against observation noise propagation introduced by spatiotemporal modeling. Moreover, we introduce an adaptive training strategy by formulating multi-adversarial learning as a multi-task learning problem. Finally, extensive experiments on two real-world datasets show that MasterGNN achieves the best performance compared with seven baselines on both air quality and weather prediction tasks.