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In this work, the ignition delay times of stoichiometric methane/dimethyl ether (DME) were measured behind the reflected shock waves over a wide range of conditions: temperatures between 1134 and 2105 K, pressures of 1, 5, and 10 bar, a DME blending ratio from 0 to 100% (M100 to M0), and an argon concentration of 95%. The present shock tube facility was validated by comparing the measured ignition delay times of DME with literature values and was used for measurement of the subsequent methane/DME ignition delay times. The ignition delay times of all mixtures exhibit a negative pressure dependence. For a given temperature, the ignition delay time of methane/DME decreases remarkably with the presence of only 1% DME. As the DME blending ratio increases, the ignition delay times are correspondingly decreased; however, the ignition promotion effect of DME is decreased. The calculated ignition delay times of methane/DME mixtures using two recently developed kinetic mechanisms are compared with those of measurements. The NUI C4 mechanism yields good prediction for the ignition delay time of methane. With an increase of the DME blending ratio, the performance of this model becomes moderated. Zhao’s DME model yields good prediction for all of the mixtures studied in this work; thus, it was selected for analyzing the ignition kinetics of methane/DME fuel blends, through which the nonlinear effect of DME addition in promoting ignition is interpreted.