The phase behavior of the binary systems consisting of the organic solvent diethyl methylphosphonate (DEMP) and the gases carbon dioxide (CO2) and methane (CH4) is experimentally studied. A synthetic method is used to measure the solubilities. Bubble-point pressures of the system DEMP + CO2 are reported for CO2 concentrations ranging from (15.40 to 86.44) mole % and within a temperature range of (283.4 to 338.1) K and compared to the limited experimental data in the literature. Also, bubble-point pressures of the system DEMP + CH4 are reported for CH4 concentrations ranging from (5.17 to 15.30) mole % and within a temperature range of (283.2 to 358.5) K, which have never been measured before. The solubilities of CH4 are much lower than the solubilities of CO2 in DEMP. Moreover, the temperature has a much larger influence on the CO2 solubility in DEMP compared to the effect of temperature on the CH4 solubility.