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The minimisation of tail-pipe emissions and fuel consumption during cold-start can be viewed as a constrained optimisation problem involving many parameters. Examining this problem mathematically first requires an accurate and computationally practical model of the engine and exhaust system. This paper proposes such a model for use during the cold-start of a conventional spark ignition engine. This model uses as much physics-based modelling as is computationally practical for optimisation and control studies. It takes a given set of engine control inputs to simulate tailpipe CO , HC and NO emissions, and is both calibrated and validated using detailed measurements obtained on a transient engine dynamometer following the New European Drive Cycle (NEDC).