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In this paper, we propose a Hierarchical Learned Video Compression (HLVC) method with three hierarchical quality layers and a recurrent enhancement network. The frames in the first layer are compressed by an image compression method with the highest quality. Using these frames as references, we propose the Bi-Directional Deep Compression (BDDC) network to compress the second layer with relatively high quality. Then, the third layer frames are compressed with the lowest quality, by the proposed Single Motion Deep Compression (SMDC) network, which adopts a single motion map to estimate the motions of multiple frames, thus saving bits for motion information. In our deep decoder, we develop the Weighted Recurrent Quality Enhancement (WRQE) network, which takes both compressed frames and the bit stream as inputs. In the recurrent cell of WRQE, the memory and update signal are weighted by quality features to reasonably leverage multi-frame information for enhancement. In our HLVC approach, the hierarchical quality benefits the coding efficiency, since the high quality information facilitates the compression and enhancement of low quality frames at encoder and decoder sides, respectively. Finally, the experiments validate that our HLVC approach advances the state-of-the-art of deep video compression methods, and outperforms the "Low-Delay P (LDP) very fast" mode of x265 in terms of both PSNR and MS-SSIM. The project page is at https://github.com/RenYang-home/HLVC.