A real-time zero-dimensional diagnostic combustion model has been developed and assessed to evaluate in-cylinder temperatures, HRR (heat release rate) and NOx (nitrogen oxides) in DI (Direct Injection) diesel engines under steady state and transient conditions. The approach requires very little computational time, that is, of the order of a few milliseconds, and is therefore suitable for real-time applications. It could, for example, be implemented in an ECU (Engine Control Unit) for the on-board diagnostics of combustion and emission formation processes, or it could be integrated in acquisition software installed on an engine test bench for indicated analysis. The model could also be used for post-processing analysis of previously acquired experimental data. The methodology is based on a three-zone thermodynamic model: the combustion chamber is divided into a fuel zone, an unburned gas zone and a stoichiometric burned gas zone, to which the energy and mass conservation equations are applied. The main novelty of the proposed method is that the equations can be solved in closed form, thus making the approach suitable for real-time applications. The evaluation of the temperature of burned gases allows the in-cylinder NOx concentration to be calculated, on the basis of prompt and Zeldovich thermal mechanisms. The procedure also takes into account the NOx level in the intake charge, and is therefore suitable for engines equipped with traditional short-route EGR (Exhaust Gas Recirculation) systems, and engines equipped with SCR (Selective Catalytic Reduction) and long-route EGR systems. The diagnostic model was tested on a GMPT-E Euro 5 diesel engine, under both steady-state and fast transient conditions. The experimental data were acquired at the dynamic test bench of ICEAL-PT (Internal Combustion Engine Advanced Laboratory at the Politecnico di Torino). (C) 2014 Elsevier Ltd. All rights reserved.