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Multi-task learns multiple tasks, while sharing knowledge and computation among them. However, it suffers from catastrophic forgetting of previous knowledge when learned incrementally without access to the old data. Most existing object detectors are domain-specific and static, while some are learned incrementally but only within a single domain. Training an object detector incrementally across various domains has rarely been explored. In this work, we propose three incremental learning scenarios across various domains and categories for object detection. To mitigate catastrophic forgetting, attentive feature distillation is proposed to leverages both bottom-up and top-down attentions to extract important information for distillation. We then systematically analyze the proposed distillation method in different scenarios. We find out that, contrary to common understanding, domain gaps have smaller negative impact on incremental detection, while category differences are problematic. For the difficult cases, where the domain gaps and especially category differences are large, we explore three different exemplar sampling methods and show the proposed adaptive sampling method is effective to select diverse and informative samples from entire datasets, to further prevent forgetting. Experimental results show that we achieve the significant improvement in three different scenarios across seven object detection benchmark datasets.