Abstract Partial least squares (PLS) is a powerful and frequently applied technique for process modelling and monitoring when the data is highly correlated. In this paper, a Box–Tidwell transformation based PLS (BTPLS) algorithm is proposed to address the modelling of non-linear systems. The BTPLS algorithm provides a family of flexible regression models for data fitting, where linear and quadratic PLS are special cases. BTPLS is shown to out-perform quadratic PLS, for non-linear problems, in terms of modelling ability and prediction accuracy, and neural network based PLS algorithms with respect to computational time and model parsimony in terms of the Bayesian information criterion. Linear PLS, quadratic PLS, neural network PLS and BTPLS are compared using a benchmark data set relating to the analysis of cosmetic data, a mathematical simulation and a highly non-linear pH problem. It is shown that the BTPLS algorithm provides a pragmatic compromize between model simplicity and accuracy, and constitutes a complementary modelling technique to both existing linear and non-linear PLS approaches.