This is Part II of a series of three papers which jointly address the combustion chemistry of furan and its alkylated derivatives 2-methylfuran (MF) and 2,5-dimethylfuran (DMF) under premixed low-pressure flame conditions. Some of them are considered to be promising biofuels. With furan as a common basis studied in Part I of this series, the present paper addresses two laminar premixed low-pressure (20 and 40 mbar) flat argon-diluted (50%) flames of MF which were studied with electron ionization molecular-beam mass spectrometry (EI-MBMS) and gas chromatography (GC) for equivalence ratios phi = 1.0 and 1.7, identical conditions to those for the previously reported furan flames. Mole fractions of reactants, products as well as stable and reactive intermediates were measured as a function of the distance above the burner. Kinetic modeling was performed using a comprehensive reaction mechanism for all three fuels given in Part I and described in the three parts of this series. A comparison of the experimental results and the simulation shows reasonable agreement, as also seen for the furan flames in Part I before. This set of experiments is thus considered to be a valuable additional basis for the validation of the model. The main reaction pathways of MF consumption have been derived from reaction flow analyses, and differences to furan combustion chemistry under the same conditions are discussed.