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The Dry-Low-NOx (DLN) Micromix combustion technology has been developed as low emission combustion principle for industrial gas turbines fueled with hydrogen or syngas. The combustion process is based on the phenomenon of jet-in-crossflow-mixing (JICF). Fuel is injected perpendicular into the air-cross-flow and burned in a multitude of miniaturized, diffusion-like flames. The miniaturization of the flames leads to a significant reduction of NOx emissions due to the very short residence time of reactants in the flame. In the Micromix research approach, computational fluid dynamics (CFD) analyses are validated toward experimental results. The combination of numerical and experimental methods allows an efficient design and optimization of DLN Micromix combustors concerning combustion stability and low NOx emissions. The paper presents a comparison of several numerical combustion models for hydrogen and hydrogen-rich syngas. They differ in the complexity of the underlying reaction mechanism and the associated computational effort. The performance of a hybrid eddy-break-up (EBU) model with a one-step global reaction is compared to a complex chemistry model and a flamelet generated manifolds (FGM) model, both using detailed reaction schemes for hydrogen or syngas combustion. Validation of numerical results is based on exhaust gas compositions available from experimental investigation on DLN Micromix combustors. The conducted evaluation confirms that the applied detailed combustion mechanisms are able to predict the general physics of the DLN-Micromix combustion process accurately. The FGM method proved to be generally suitable to reduce the computational effort while maintaining the accuracy of detailed chemistry.