In this paper a novel identification algorithm for a class of non-linear, possibly parameter varying models is proposed. The algorithm is based on separable least squares ideas. These models are given in the form of a linear fractional transformation (LIFT) where the 'forward' part is represented by a conventional linear regression and the 'feedback' part is given by a non-linear map which can take into account scheduling variables available for measurement. The non-linear part of the model can be parameterized according to various paradigms, like, e.g. neural network (NN) or general nonlinear autoregressive exogenous (NARX) models. The estimation algorithm exploits the separability of the criterion used to estimate the parameters. When using a NN, it is possible the explicit computation of the Frechet derivative needed to implement a separable least square algorithm.