Projection to latent structures (PLS) has been shown to be a robust multivariate linear regression technique for the analysis and modelling of noisy and highly correlated data. It has been successfully applied in the modelling, prediction and statistical control of the behaviour of a wide variety of processes. However, many chemical and physical systems display non-linear behaviour which cannot be reliably modelled by means of linear regression techniques. A number of different approaches have been proposed to provide a non-linear PLS algorithm by incorporating non-linear features within the linear PLS framework. In this paper the traditional linear PLS algorithm and the non-linear (quadratic) PLS approach of Weld are reviewed, prior to introducing a number of modifications into the non-linear quadratic algorithm to improve its performance when handling highly non-linear data. The existing and modified algorithms are applied and compared on three data sets: a highly non-linear mathematical function; an industrial pH simulation problem; and finally on data from an industrial fluidised-bed reactor.