Gasoline-controlled auto ignition is a promising technology capable of reducing both fuel consumption and emissions at the same time. There are, however, challenges to overcome in order to make practical use of it. One area of research addresses methods that guarantee stable combustion as gasoline-controlled auto ignition is very sensitive to disturbances. This article investigates the capability of nonlinear model predictive control to ensure stable combustion while maintaining efficient operation. For this purpose, a suitable gasoline-controlled auto ignition model is selected and identified using measurement data of a single-cylinder test bed. Building upon this model, a controller based on nonlinear model predictive control is derived and analyzed by means of simulation. The investigation shows that the control manages to follow prescribed set points, also for late combustion, and indicates promising results with respect to real-time computation constraints.