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The paper describes a numerical study of the combustion of hydrogen enriched methane and biogases containing hydrogen in a Controlled Auto Ignition engine (CAI). A single cylinder CAI engine is modelled with Chemkin to predict engine performance, comparing the fuels in terms of indicated mean effective pressure, engine efficiency, and pollutant emissions. The effects of hydrogen and carbon dioxide on the combustion process are evaluated using the GRI-Mech 3.0 detailed radical chain reactions mechanism. A parametric study, performed by varying the temperature at the start of compression and the equivalence ratio, allows evaluating the temperature requirements for all fuels; moreover, the effect of hydrogen enrichment on the auto-ignition process is investigated. The results show that, at constant initial temperature, hydrogen promotes the ignition, which then occurs earlier, as a consequence of higher chemical reactivity. At a fixed indicated mean effective pressure, hydrogen presence shifts the operating range towards lower initial gas temperature and lower equivalence ratio and reduces NOx emissions. Such reduction, somewhat counter-intuitive if compared with similar studies on spark-ignition engines, is the result of operating the engine at lower initial gas temperatures.