In this paper, a fully real-time implementable constrained Nonlinear Model Predictive Control (NMPC) is proposed for the control of a Diesel engine air path. The resulting control scheme is a discrete-time output feedback based on nonlinear receding-horizon observer. Unlike existing approaches addressing the same problem, the proposed NMPC is not based on any kind of linear per mode modeling paradigm and can therefore be easily extended to more elaborated nonlinear models.