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Abstract: For nonlinear processes the classical model predictive control (MPC) algorithm, in which a linear model is used, usually does not give satisfactory closed-loop performance. In such nonlinear cases a suboptimal MPC strategy is typically used in which the nonlinear model is successively linearised on-line for the current operating point and, thanks to linearisation, the control policy is calculated from a quadratic programming problem. Although the suboptimal MPC algorithm frequently gives good results, for some nonlinear processes it would be beneficial to further improve control accuracy. This paper details a computationally efficient nonlinear MPC algorithm in which a neural model is linearised on-line along the predicted trajectory in an iterative way. The algorithm needs solving on-line only a series of quadratic programming problems. Advantages of the discussed algorithm are demonstrated in the control system of a high-purity ethylene–ethane distillation column for which the classical linear MPC algorithm does not work and the classical suboptimal MPC algorithm is slow. It is shown that the discussed algorithm can give practically the same control accuracy as the algorithm with on-line nonlinear optimisation and, at the same time, the algorithm is significantly less computationally demanding. [Copyright &y& Elsevier]