Although SCR is a well established technology for many applications, it is still a field in which several new approaches and components are being tested. Control is a critical issue, as the conflicting requirements of NOx abatement and very small NH3 slip need to be met. Besides empirical solutions, model based controls have been proposed and are probably the technology of choice, also in view of the combination with monitoring functions. However, SCR models are typically based on First Principles (FP), i.e. on global chemical equations and reaction rate equations, and require precise calibration. Still, their performance for the control of dynamic processes is limited, or a high detail, much a priori information, e.g. on the actual SCR reaction rates, are needed. Frequently, this information is not available or reliable, and this is particularly true when components are changed or modified during the development process, so that typically a re-design is needed.Against this background, this paper proposes a grey box approach, in which a simple first principle model is used as basic model, without assuming any special information on the physical parameters, (e.g. the above mentioned actual SCR reaction rates). On the contrary, these parameters, in particular the actual reaction rates are to be determined by an optimization technique using measurements under real operation conditions on a test bench with the engine and the whole exhaust after treatment system. In order to account for those effects which are not properly modeled by the simple first principle approach, an extension of the model using an output error model is shown to attain satisfactory performance for the complete operation ranges of the SCR. Finally, the whole model was experimentally validated in a dynamical test cycle and under different dynamical operating conditions.