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Methanol, MeOH, is one of the most attractive alternative fuels for internal combustion engines. In diesel applications, methanol's poor ignition properties necessitate the use of expensive additives for ignition improvement [1]. Dimethyl ether, DME, as a combustion improver for methanol, was recently evaluated in [2]. This study is directed towards a better understanding of the auto-ignition and combustion of a blend fuel composition consisting of liquid methanol and gaseous dimethyl ether aspirated with the combustion air by using the results of numerical simulation. The numerical model was based on the computer code KIVA-3. The computational results show that the use of DME as an ignition improver is only reasonable for gas temperatures below 900 K. At typical diesel conditions, an amount of DME in a quantity less than 10-15 volumetric percent of oxygen content in the combustion volume is sufficient for ignition improvement.