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Hyperspectral imaging, capturing detailed spectral information for each pixel, is pivotal in diverse scientific and industrial applications. Yet, the acquisition of high-resolution (HR) hyperspectral images (HSIs) often needs to be addressed due to the hardware limitations of existing imaging systems. A prevalent workaround involves capturing both a high-resolution multispectral image (HR-MSI) and a low-resolution (LR) HSI, subsequently fusing them to yield the desired HR-HSI. Although deep learning-based methods have shown promising in HR-MSI/LR-HSI fusion and LR-HSI super-resolution (SR), their substantial model complexities hinder deployment on resource-constrained imaging devices. This paper introduces a novel knowledge distillation (KD) framework for HR-MSI/LR-HSI fusion to achieve SR of LR-HSI. Our KD framework integrates the proposed Cross-Layer Residual Aggregation (CLRA) block to enhance efficiency for constructing Dual Two-Streamed (DTS) network structure, designed to extract joint and distinct features from LR-HSI and HR-MSI simultaneously. To fully exploit the spatial and spectral feature representations of LR-HSI and HR-MSI, we propose a novel Cross Self-Attention (CSA) fusion module to adaptively fuse those features to improve the spatial and spectral quality of the reconstructed HR-HSI. Finally, the proposed KD-based joint loss function is employed to co-train the teacher and student networks. Our experimental results demonstrate that the student model not only achieves comparable or superior LR-HSI SR performance but also significantly reduces the model-size and computational requirements. This marks a substantial advancement over existing state-of-the-art methods. The source code is available at https://github.com/ming053l/CSAKD., Comment: Submitted to TIP 2024