Environmental regulations are continuously raising the bar towards more advanced diesel engine designs ca- pable of minimizing the emissions of polluting substances. The recent IMO Tier III legislation, entered into force in 2016, is forcing the engine manufacturers to meet a NOx reduction of more than 70% from Tier II for all the ships sailing in designated NOx Emission Control Areas (NECA). Although these zones are, up to now, limited to the North American and U.S. Caribbean Sea NECAs, future regions, such as the North Sea and Baltic NECA in 2021 as well as stricter national and port regulations, are increasing the uncertainty regarding the possible compliance methods. The Selective Catalytic Reduction (SCR) represents a flexible, proven and commercially available technology capable of reducing more than 80% of the NOx in the exhaust gas. Its adoption started in the ’70s and was aimed at the reduction of stationary source emissions. From early 2000, it has been extended to the automotive industry in order to meet the Euro and EPA legislation for heavy duty and light diesel engines. Despite the evident disadvantages of the high installation cost and the considerable space requirements, the application of the SCR is subjected to a number of operating limits such as the narrow optimal temperature window and the slip of byproducts originated from the chemical reactions. These limitations can be even more severe when the diesel engine undergoes transient and dynamic operations. The main objective of this research is to gain insights into the behaviour of the SCR technology under steady-state and dynamic operations of the diesel engine. After an accurate literature review of the working principles, reaction kinetics and modeling approach, a first principle model of the SCR has been developed to fulfill the scope. A 1D single channel approach, discretized along the reactor length, has been adopted to sim- ulate the heat exchange and the chemical reactions occurring in the catalyst. To facilitate the integration of the designed model with an existing diesel engine model available in the Maritime and Transport Technology Department of the 3me faculty, the resistance and volume approach has been selected. After the verification of the SCR model, the integrated system "SCR+Engine" has been tested under steady-state conditions, to an- alyze the effect that the added back pressure has on the engine performance, and under dynamic conditions, to simulate "real" load case scenarios that the SCR might experience. The designed model, although limited from the chemical reaction point of view, is able to predict NOx reduction and ammonia slip under steady-state and transient operations. It can be further used in an early design phase to investigate the feasibility of the SCR inclusion in the drive trains of ships. Future studies are recommended to optimize the model, by taking into account the sulphur influence on the reduction efficiency and the catalyst aging, and to validate it with real experiments on marine SCR systems.