In this letter, the capabilities of feedforward neural networks (FNNs) on the realization and approximation of functions of the form g: R 1 → A, which partition the R 1 space into polyhedral sets, each one being assigned to one out of the c classes of A , are investigated. More specifically, a constructive proof is given for the fact that FNNs consisting of nodes having sigmoid output functions are capable of approximating any function g with arbitrary accuracy. Also, the capabilities of FNNs consisting of nodes having the hard limiter as output function are reviewed. In both cases, the two-class as well as the multiclass cases are considered.