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A new technique, called inter-band compensated prediction, for coding colour and multispectral images is presented. It is suitable to use for coding any spectral domain and can code colour and multispectral images with any number of bands. This technique is based on the same principles as the very efficient motion compensated prediction largely used in video coding. Thus, each band is predicted in the spectral direction by compensating the differences in the neighbouring bands and then coding the prediction error spatially by another method. This is a forward adaptive prediction and the information used for compensation is coded as side information with prediction error. The comparison of the coding results with the state-of-the-art coding algorithms, based on spectral transformations, proves that this technique is very efficient and can even outperform them. In addition, compensation can be combined with any spatial coder that allows lossless, lossy and scalable coding of any spectral content of the image. It has also the advantages of being simple to implement and to use with parallel architectures.