Object detectors do not work well when domains largely differ between training and testing data. To solve this problem, domain generalization approaches, which require training data with ground-truth labels from multiple domains, have been proposed. However, it is time-consuming and labor-intensive to collect those data for object detection because not only class labels but also bounding boxes must be annotated. To overcome the problem of domain gap in object detection without requiring expensive annotations, we propose to consider two new problem settings: semi-supervised domain generalizable object detection (SS-DGOD) and weakly-supervised DGOD (WS-DGOD). In contrast to the conventional domain generalization for object detection that requires labeled data from multiple domains, SS-DGOD and WS-DGOD require labeled data only from one domain and unlabeled or weakly-labeled data from multiple domains for training. We show that object detectors can be effectively trained on the proposed settings with the same student-teacher learning framework, where a student network is trained with pseudo labels output from a teacher on the unlabeled or weakly-labeled data. The experimental results demonstrate that the object detectors trained on the proposed settings significantly outperform baseline detectors trained on one labeled domain data and perform comparably to or better than those trained on unsupervised domain adaptation (UDA) settings, while ours do not use target domain data for training in contrast to UDA.