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Image super-resolution (SR) usually synthesizes degraded low-resolution images with a predefined degradation model for training. Existing SR methods inevitably perform poorly when the true degradation does not follow the predefined degradation, especially in the case of the real world. To tackle this robustness issue, we propose a cascaded degradation-aware blind super-resolution network (CDASRN), which not only eliminates the influence of noise on blur kernel estimation but also can estimate the spatially varying blur kernel. With the addition of contrastive learning, our CDASRN can further distinguish the differences between local blur kernels, greatly improving its practicality. Experiments in various settings show that CDASRN outperforms state-of-the-art methods on both heavily degraded synthetic datasets and real-world datasets.