Minimum variance and (MV) and generalised minimum variance (GMV) control methods are studied with respect to a particular class of nonlinear input/output recursive models. The plant model is affine in the most recent control variable. Prediction form models are introduced and nonlinear MV/GMV control design techniques are developed based on these. Suitable neural networks are employed for the estimation of the nonlinearities of the system. The weights of the networks are estimated offline and the learning is carried out with input/output data provided by suitable open-loop identification experiments. The MV/GMV controllers obtained are composed of linear and nonlinear blocks, the latter being implemented with neural networks. The linear blocks can be tuned online to improve the controlled system performance. A satisfactory performance is generally obtained in a wide operation range, with convenient dynamical behaviour and low control effort. A discussion on the presence of offset errors is presented and some possible rejection methods are proposed.