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Recently, adversarial-based domain adaptive object detection (DAOD) methods have been developed rapidly. However, there are two issues that need to be resolved urgently. Firstly, numerous methods reduce the distributional shifts only by aligning all the feature between the source and target domain, while ignoring the private information of each domain. Secondly, DAOD should consider the feature alignment on object existing regions in images. But redundancy of the region proposals and background noise could reduce the domain transferability. Therefore, we establish a Feature Separation and Alignment Network (FSANet) which consists of a gray-scale feature separation (GSFS) module, a local-global feature alignment (LGFA) module and a region-instance-level alignment (RILA) module. The GSFS module decomposes the distractive/shared information which is useless/useful for detection by a dual-stream framework, to focus on intrinsic feature of objects and resolve the first issue. Then, LGFA and RILA modules reduce the distributional shifts of the multi-level features. Notably, scale-space filtering is exploited to implement adaptive searching for regions to be aligned, and instance-level features in each region are refined to reduce redundancy and noise mentioned in the second issue. Various experiments on multiple benchmark datasets prove that our FSANet achieves better performance on the target domain detection and surpasses the state-of-the-art methods.