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A new neural tree model, called adaptive high-order neural tree (AHNT), is proposed for classifying large sets of multidimensional patterns. The AHNT is built by recursively dividing the training set into subsets and by assigning each subset to a different child node. Each node is composed of a high-order perceptron (HOP) whose order is automatically tuned taking into account the complexity of the pattern set reaching that node. First-order nodes divide the input space with hyperplanes, while HOPs divide the input space arbitrarily, but at the expense of increased complexity. Experimental results demonstrate that the AHNT generalizes better than trees with homogeneous nodes, produces small trees and avoids the use of complex comparative statistical tests and/or a priori selection of large parameter sets.