AbstractThe aim of this paper is to propose a novel class of non‐linear, possibly parameter‐varying models suitable for system identification purposes. These models are given in the form of a linear fractional transformation (LFT) where the ‘forward’ part is represented by a conventional linear regression and the ‘feedback’ part is given by a non‐linear dynamic map parameterized by a neural network (NN) which can take into account scheduling variables available for measurement.For this specific model structure a parameter estimation procedure has been set up, which turns out to be particularly efficient from the computational point of view. Also, it is possible to establish a connection between this model class and the well known class of local model networks (LMNs): this aspect is investigated in the paper. Finally, we have applied the proposed identification procedure to the problem of determining accurate non‐linear models for knee joint dynamics in paraplegic patients, within the framework of a functional electrical stimulation (FES) rehabilitation engineering project. Copyright © 2002 John Wiley & Sons, Ltd.