Title: Weakly-Supervised Domain Adaptation in Federated Learning. Abstract: Federated domain adaptation (FDA) describes the setting where a set of source clients seek to optimize the performance of a target client. To be effective, FDA must address some of the distributional challenges of Federated learning (FL). For instance, FL systems exhibit distribution shifts across clients. Further, labeled data are not always available among the clients. To this end, we propose and compare novel approaches for FDA, combining the few labeled target samples with the source data when auxiliary labels are available to the clients. The in-distribution auxiliary information is included during local training to boost out-of-domain accuracy. Also, during fine-tuning, we devise a simple yet efficient gradient projection method to detect the valuable components from each source client model towards the target direction. The extensive experiments on medical imaging datasets show that our proposed framework significantly improves federated domain adaptation performance.