N-tuple neural networks (NTNNs) have been successfully applied to both pattern recognition and function approximation tasks. Their main advantages include a single layer structure, capability of realizing highly non-linear mappings and simplicity of operation. In this work a modification of the basic network architecture is presented, which allows it to operate as a non-parametric kernel regression estimator. This type of network is inherently capable of approximating complex probability density functions (pdfs) and, in the limiting sense, deterministic arbitrary function mappings. At the same time, the regression network features a powerful one-pass training procedure and its learning is statistically consistent. The major advantage of utilizing the N-tuple architecture as a regression estimator is the fact that in this realization the training set points are stored by the network implicitly, rather than explicitly, and thus the operation speed remains constant and independent of the training set size. Therefore, the network performance can be guaranteed in practical implementations. Copyright 1996 Elsevier Science Ltd