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We propose a novel domain adaptive action detection approach and a new adaptation protocol that leverages the recent advancements in image-level unsupervised domain adaptation (UDA) techniques and handle vagaries of instance-level video data. Self-training combined with cross-domain mixed sampling has shown remarkable performance gain in semantic segmentation in UDA (unsupervised domain adaptation) context. Motivated by this fact, we propose an approach for human action detection in videos that transfers knowledge from the source domain (annotated dataset) to the target domain (unannotated dataset) using mixed sampling and pseudo-label-based selftraining. The existing UDA techniques follow a ClassMix algorithm for semantic segmentation. However, simply adopting ClassMix for action detection does not work, mainly because these are two entirely different problems, i.e., pixel-label classification vs. instance-label detection. To tackle this, we propose a novel action instance mixed sampling technique that combines information across domains based on action instances instead of action classes. Moreover, we propose a new UDA training protocol that addresses the long-tail sample distribution and domain shift problem by using supervision from an auxiliary source domain (ASD). For the ASD, we propose a new action detection dataset with dense frame-level annotations. We name our proposed framework as domain-adaptive action instance mixing (DA-AIM). We demonstrate that DA-AIM consistently outperforms prior works on challenging domain adaptation benchmarks. The source code is available at https://github.com/wwwfan628/DA-AIM.