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This letter presents an original approach that exploits classified spectral prediction for lossless/near-lossless hyperspectral-image compression. Minimum-mean-square-error spectral predictors are calculated, one for each small spatial block of each band, and are classified (clustered) to yield a user-defined number of prototype predictors that are capable of matching the spectral features of different classes of pixel spectra for each wavelength. Such predictors are used to achieve a prediction, either crisp or fuzzy. Unlike most of the methods reported in the literature, the proposed approach exploits a purely spectral prediction that is suitable in compressing the data in band-interleaved-by-line format, as they are available at the output of the onboard instrument. In that case, the training phase, i.e., clustering and refining of predictors for each wavelength, may be moved offline. Experimental results on Airborne Visible InfraRed Imaging Spectrometer data show improvements over the most advanced methods in the literature, with a computational complexity that is far lower than that of analogous methods by the same and other authors.