This paper presents a combined nonlinear model predictive control and moving horizon estimation strategy for active surge control in compression systems. The main advantage of using model predictive control is the ability to include constraints, particularly on the actuators. The manipulated variables represent the pressure drop across the close-coupled valve (CCV) and the torque applied to the compressor shaft. Both manipulated variables are limited in magnitude and rate of change for real compression systems. Only positive values are feasible for both of them, for example. The performance of the control and estimation strategy is demonstrated in numerical simulations with added measurement and process noises.