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Detectors trained with massive labeled data often exhibit dramatic performance degradation in some particular scenarios with data distribution gap. To alleviate this problem of domain shift, conventional wisdom typically concentrates solely on reducing the discrepancy between the source and target domains via attached domain classifiers, yet ignoring the difficulty of such transferable features in coping with both classification and localization subtasks in object detection. To address this issue, in this paper, we propose Task-specific Inconsistency Alignment (TIA), by developing a new alignment mechanism in separate task spaces, improving the performance of the detector on both subtasks. Specifically, we add a set of auxiliary predictors for both classification and localization branches, and exploit their behavioral inconsistencies as finer-grained domain-specific measures. Then, we devise task-specific losses to align such cross-domain disagreement of both subtasks. By optimizing them individually, we are able to well approximate the category- and boundary-wise discrepancies in each task space, and therefore narrow them in a decoupled manner. TIA demonstrates superior results on various scenarios to the previous state-of-the-art methods. It is also observed that both the classification and localization capabilities of the detector are sufficiently strengthened, further demonstrating the effectiveness of our TIA method. Code and trained models are publicly available at https://github.com/MCG-NJU/TIA.