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Application of Gaussian-synapse-based artificial neural networks to detection and unmixing of endmembers within hyperspectral images is the objective of this paper, particularly in cases where some of them are mixed in a low ratio, which is usually the case in target detection problems. These networks and the training algorithm developed are very efficient in the determination of the abundance of the different endmembers present in the data using a very small training set that can be obtained without any knowledge on the proportions of the endmembers present. Validation and test of these networks are carried out through their application to a benchmark set of artificially generated hyperspectral images containing five endmembers with spatially diverse abundance. As a second test, we applied the strategy to a real image and checked its behavior in regions where there were transitions between zones that were differently labeled, and we compared this strategy to a hypothetical evolution of the spectrum from the endmember in one of the regions to the endmember in the other. A very good correspondence was found.