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Learned video compression has recently emerged as an essential research topic in developing advanced video compression technologies, where motion compensation is considered one of the most challenging issues. In this paper, we propose a learned video compression framework via heterogeneous deformable compensation strategy (HDCVC) to tackle the problems of unstable compression performance caused by single-size deformable kernels in downsampled feature domain. More specifically, instead of utilizing optical flow warping or single-size-kernel deformable alignment, the proposed algorithm extracts features from the two adjacent frames to estimate content-adaptive heterogeneous deformable (HetDeform) kernel offsets. Then we transform the reference features with the HetDeform convolution to accomplish motion compensation. Moreover, we design a Spatial-Neighborhood-Conditioned Divisive Normalization (SNCDN) to achieve more effective data Gaussianization combined with the Generalized Divisive Normalization. Furthermore, we propose a multi-frame enhanced reconstruction module for exploiting context and temporal information for final quality enhancement. Experimental results indicate that HDCVC achieves superior performance than the recent state-of-the-art learned video compression approaches.