A nonlinear extension of minimum variance and generalised minimum variance control strategies is developed. The plant is modelled with a linear autoregressive part and a nonlinear dependency on the input. A neural network based implementation of the control law is discussed. This results in a nonlinear controller constituted by a few linear blocks complemented with not more than two neural networks. The weights of the networks are estimated off-line and the learning is carried out with input-output data provided by suitable open loop identification experiments. The performance of the time-invariant neuro-control system is compared with the one achievable by adaptive controllers based on linar models of the plant.