Vapor-liquid equilibrium (VLE) measurements of the (CO2 + CH4) system are reported along seven isotherms at temperatures varying from just above the triple point to just below the critical point of CO2 at pressures from the vapor pressure of pure CO2 to approximately 9 MPa, including near-critical states. From these data, the critical locus has been determined and correlated over its entire length. The VLE data are correlated with the Peng-Robinson equation of state (PR-EoS), using a temperature-dependent binary interaction parameter, and also compared with the predictions of the GERG-2008 equation of state. The former represents the phase compositions across all isotherms with a root-mean-square mole-fraction deviation of S = 0.0075 while, for the latter, S = 0.0126. Measurements of the three-phase solid-vapor-liquid equilibrium (SVLE) line are reported at temperatures from approximately (204 to 216) K and a new correlation is developed which is valid from 145 K to the triple point of CO2. Additionally, we report the partitioning of trace levels of H2S between coexisting liquid and vapor phases of the (CO2 + CH4) system and compare the results with the predictions of the PR-EoS.