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Efficient and effective real-world image super-resolution (Real-ISR) is a challenging task due to the unknown complex degradation of real-world images and the limited computation resources in practical applications. Recent research on Real-ISR has achieved significant progress by modeling the image degradation space; however, these methods largely rely on heavy backbone networks and they are inflexible to handle images of different degradation levels. In this paper, we propose an efficient and effective degradation-adaptive super-resolution (DASR) network, whose parameters are adaptively specified by estimating the degradation of each input image. Specifically, a tiny regression network is employed to predict the degradation parameters of the input image, while several convolutional experts with the same topology are jointly optimized to specify the network parameters via a non-linear mixture of experts. The joint optimization of multiple experts and the degradation-adaptive pipeline significantly extend the model capacity to handle degradations of various levels, while the inference remains efficient since only one adaptively specified network is used for super-resolving the input image. Our extensive experiments demonstrate that the proposed DASR is not only much more effective than existing methods on handling real-world images with different degradation levels but also efficient for easy deployment. Codes, models and datasets are available at https://github.com/csjliang/DASR.