A new apparatus for the study of vapor-liquid or vapor-liquid-liquid equilibrium has been assembled. The apparatus, based on a static and analytical method, can perform measurements at temperatures from 185 to 320 K and pressures up to 8 MPa. The equilibrium vapor pressures of (xenon + methane) binary mixtures have been measured at seven temperatures, from 189.78 to 273.18 K, and at pressures up to 6.8 MPa. The mixture critical line has been estimated and found to be continuous between the critical points of the pure components. The system is found to display type I behavior in the classification scheme of Scott and van Konynenburg. The results have been correlated by the Peng-Robinson equation of state and a more rigorous theoretical study performed with the statistical associating fluid theory for potentials of variable range (SAFT-VR).