Laminar flame speeds of dimethyl ether and dimethoxymethane at pressures from 1 to 5 bar and initial temperatures from 298 to 373 K were determined experimentally using a constant volume spherical vessel and a heat flux burner setup. This study is the first to report dimethoxymethane laminar flame speeds at a pressure higher than 1 bar. Using these experimental data along with data available in the literature, a new kinetic model for the prediction of the oxidation behavior of dimethyl ether and dimethoxymethane in freely propagating and burner stabilized premixed flames, in shock tubes, rapid compression machines, flow reactors, and a jet-stirred reactor has been developed. The experimental results from the present work and literature are interpreted with the help of the derived kinetic model. This newly developed reaction mechanism considers the redox chemistry of NOx to accommodate the influence of the oxygen level on the onset of fuel conversion and interconversion of NO and NO2. The current model suggests that an increased O2 level promotes the HO2 production, which in turn leads to the formation of OH radicals, which promotes the combustion of the fuel/air mixture under lean conditions. The increase of OH radical concentrations is mainly via the NO/NO2 interconversion reaction channel, NO+HO2=NO2+OH, NO2+H=NO+OH, CH3OCH3+NO2=CH3OCH2+HONO, followed by the thermal decomposition of HONO. This work extends the kinetic database and helps to improve the understanding of dimethyl ether and dimethoxymethane combustion behavior. The kinetic model presented in this work can serve as a base model for hydrocarbons and oxygenated fuels higher than C2.