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In the last decades, NOx emissions legislations for Diesel engines are becoming more stringent than ever before and the selective catalytic reduction (SCR) is considered as the most suitable technology to comply with the upcoming constraints. Model-based control strategies are promising to meet the dual objective of maximizing NOx reduction and minimizing NH3 slip in urea-selective catalytic reduction. In this paper, a control oriented model of a Cu-zeolite urea-SCR system for automotive diesel engines is presented. The model is derived from a quasi-dimensional four-state model of the urea-SCR plant. To make it suitable for the real-time urea-SCR management, a reduced order one-state model has been developed, with the aim of capturing the essential behavior of the system with a low computational burden. Particularly, the model allows estimating the NH3 slip that is fundamental not only to minimize urea consumption but also to reduce this unregulated emission.