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Denoising and demosaicking are two essential steps to reconstruct a clean full-color image from the raw data. Recently, joint denoising and demosaicking (JDD) for burst images, namely JDD-B, has attracted much attention by using multiple raw images captured in a short time to reconstruct a single high-quality image. One key challenge of JDD-B lies in the robust alignment of image frames. State-of-the-art alignment methods in feature domain cannot effectively utilize the temporal information of burst images, where large shifts commonly exist due to camera and object motion. In addition, the higher resolution (e.g., 4K) of modern imaging devices results in larger displacement between frames. To address these challenges, we design a differentiable two-stage alignment scheme sequentially in patch and pixel level for effective JDD-B. The input burst images are firstly aligned in the patch level by using a differentiable progressive block matching method, which can estimate the offset between distant frames with small computational cost. Then we perform implicit pixel-wise alignment in full-resolution feature domain to refine the alignment results. The two stages are jointly trained in an end-to-end manner. Extensive experiments demonstrate the significant improvement of our method over existing JDD-B methods. Codes are available at https://github.com/GuoShi28/2StageAlign.