Four-phase equilibrium conditions (hydrate-liquid-liquid(aq)-vapor) were studied for the system methane + carbon dioxide + neohexane + water by the pressure search method. In addition, three-phase equilibrium conditions (hydrate-liquid-vapor) were determined for the same system in the absence of neohexane. Experimental conditions were varied in the temperature range of (275 to 285) K and the pressure range of (1.3 to 7.5) MPa. Equilibrium temperature and pressure values were found to agree, within the uncertainties herein reported, with existing literature values for both systems. The data were used to produce experimental contour plots that summarize the equilibrium temperature, pressure, and vapor composition on the same graph. It was observed that the equilibrium mole fraction of carbon dioxide in the vapor phase follows opposite trends in both systems, with respect to equilibrium pressure, at rather constant temperature. The data also suggest that hexagonal structure H equilibrium occurs at lower pressures and temperatures than cubic structure I (sI) when the vapor phase is methane rich; however, this phenomenon appears to be reversed as the equilibrium vapor phase becomes richer in carbon dioxide.