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Object detection for autonomous vehicles has received increasing attention in recent years, where labeled data are often expensive while unlabeled data can be collected readily, calling for research on semi-supervised learning for this area. Existing semi-supervised object detection (SSOD) methods usually assume that the labeled and unlabeled data come from the same data distribution. In autonomous driving, however, data are usually collected from different scenarios, such as different weather conditions or different times in a day. Motivated by this, we study a novel but challenging domain inconsistent SSOD problem. It involves two kinds of distribution shifts among different domains, including (1) data distribution discrepancy, and (2) class distribution shifts, making existing SSOD methods suffer from inaccurate pseudo-labels and hurting model performance. To address this problem, we propose a novel method, namely Dual-Curriculum Teacher (DucTeacher). Specifically, DucTeacher consists of two curriculums, i.e., (1) domain evolving curriculum seeks to learn from the data progressively to handle data distribution discrepancy by estimating the similarity between domains, and (2) distribution matching curriculum seeks to estimate the class distribution for each unlabeled domain to handle class distribution shifts. In this way, DucTeacher can calibrate biased pseudo-labels and handle the domain-inconsistent SSOD problem effectively. DucTeacher shows its advantages on SODA10M, the largest public semi-supervised autonomous driving dataset, and COCO, a widely used SSOD benchmark. Experiments show that DucTeacher achieves new state-of-the-art performance on SODA10M with 2.2 mAP improvement and on COCO with 0.8 mAP improvement.