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Recent years have witnessed tremendous progress in single image super-resolution (SISR) owing to the deployment of deep convolutional neural networks (CNNs). For most existing methods, the computational cost of each SISR model is irrelevant to local image content, hardware platform and application scenario. Nonetheless, content and resource adaptive model is more preferred, and it is encouraging to apply simpler and efficient networks to the easier regions with less details and the scenarios with restricted efficiency constraints. In this paper, we take a step forward to address this issue by leveraging the adaptive inference networks for deep SISR (AdaDSR). In particular, our AdaDSR involves an SISR model as backbone and a lightweight adapter module which takes image features and resource constraint as input and predicts a map of local network depth. Adaptive inference can then be performed with the support of efficient sparse convolution, where only a fraction of the layers in the backbone is performed at a given position according to its predicted depth. The network learning can be formulated as the joint optimization of reconstruction and network depth losses. In the inference stage, the average depth can be flexibly tuned to meet a range of efficiency constraints. Experiments demonstrate the effectiveness and adaptability of our AdaDSR in contrast to its counterparts (e.g., EDSR and RCAN).