Despite the remarkable performance achieved by DNN-based object detectors, class incremental object detection (CIOD) remains a challenge, in which the network has to learn to detect novel classes sequentially. Catastrophic forgetting is the main problem underlying this difficulty, as neural networks tend to detect new classes only when training samples for old classes are absent. In this paper, we propose the Replay-and-Transfer Network (RT-Net) to address this issue and accomplish CIOD. We develop a generative replay model to replay features of old classes during learning of new ones for the RoI (Region of Interest) head, using the stored latent feature distributions. To overcome the drastic changes of the RoI feature space, guided feature distillation and feature translation are introduced to facilitate knowledge transfer from the old model to the new one. In addition, we propose holistic ranking transfer, which transfers ranking orders of proposals to the new model, to enable the region proposal network to identify high quality proposals for old classes. Importantly, this framework provides a general solution for CIOD, which can be successfully applied to two task settings: set-overlapped, in which the old and new training sets are overlapped, and set-disjoint, in which the old and new tasks have unique samples. Extensive experiments on standard benchmark datasets including PASCAL VOC and COCO show that RT-Net can achieve state-of-the-art performance for CIOD.