Title: Accelerating Federated Learning Convergence via Opportunistic Mobile Relaying. Abstract: This paper studies asynchronous Federated Learning (FL) subject to clients' individual arbitrary communication patterns with the parameter server. We propose FedMobile, a new asynchronous FL algorithm that exploits the mobility attribute of the mobile FL system to improve the learning performance. The key idea is to leverage the random client-client communication in a mobile network to create additional indirect communication opportunities with the server via upload and download relaying. We prove that FedMobile achieves a convergence rate $O(\frac{1}{\sqrt{NT}})$, where $N$ is the number of clients and $T$ is the number of communication slots, and show that the optimal design involves an interesting trade-off on the best timing of relaying. Our analysis suggests that with an increased rate of client-client communication opportunities, asynchronous FL converges faster using FedMobile. Experiment results on a synthetic dataset and two real-world datasets verify our theoretical findings. 