Model Predictive Control (MPC) has been proposed several times for automotive control, with promising results, mostly based on a linear MPC approach. However, as most automotive systems are nonlinear, Nonlinear MPC (NMPC) would be an interesting option. Unfortunately, an optimal control design with a generic nonlinear model usually leads to a complex, non convex problem. Against this background, this paper presents two different schemes to take into account the system nonlinearity in the control design. First, a multi-linear MPC method is shown based on the segmentation of the system and then a control system design based on a nonlinear system identification using a quasi Linear Parameter Varying (LPV) structure is proposed, which is then used in a NMPC design framework. This paper presents the approaches and the application to a well studied system, the air path of a Diesel engine.