The pressure and temperature conditions for the four-phase equilibrium in systems that include structure-H hydrate, methane gas, liquid water, and either 3,3-dimethyl-2-butanone (pinacolone) or 3,3-dimethyl-2-butanol (pinaeolyl alcohol) liquid have been measured over the temperature range T = 273 K to T = 281 K. At a given temperature, the equilibrium pressures of the systems with pinacolone and pinacolyl alcohol are lower by 1.8 MPa and 1.3 MPa, respectively, than those of the structure-I hydrate-forming methane + water system. The equilibrium pressures in the system with pinacolone are roughly equal to those for the system with neohexane, whereas the pressures for the system with pinacolyl alcohol are higher by 0.5 MPa than those with neohexane. This suggests that the hydroxyl functional groups on the large-molecule guest substances can increase the equilibrium pressure in structure-H hydrate-forming systems, whereas the ketone groups can have little influence on the pressure.