In the paper, it is proposed to modify the known nonlinear predictive control method with a dynamic linearization around the prediction error or current process variable measurements. The approach is intended for strongly nonlinear control nonaffine processes, particularly for those that can be modeled by generalized MIMO Hammerstein models. Such models are often used, for example, for modeling various processes in chemistry. The proposed nonlinear control method allows for control constraints through including appropriate approximating functions into the model input matrix. To minimize the plant-model mismatch, an auxiliary control loop is proposed, which creates an additional control signal from the difference between the model and the plant states.