Three NMPC strategies are compared on the control of the CSTR with van der Vusse kinetics, which is largely employed in control studies. This reactor exhibits sign change of the process static gain and nonminimum phase dynamic behavior. The first strategy considers a NMPC coupled with a state estimator. The second one uses neural networks as the NMPC model. In the last one, an approach for the adaptation of the linear MPC to nonlinear systems is employed to generate predictions through successive local linearizations around steady states. The results show that the NMPC with state estimation stabilized the system at the expense of higher computational cost. The strategy based on neural networks demanded a shorter time for the calculation of the control actions, allowing the use of a shorter sampling time. The adaptive MPC stabilizes the the nonlinear system around points which are unstable under linear MPC control, demanding less computational effort than the NMPC with a state estimator