We have already reported the cage unoccupancy of hydrogen in the CO2 hydrate from the Raman spectroscopic analysis and the thermodynamic analysis using Soave - Redlich - Kwong equation of state. On the other hand, at the low temperatures, Kim and Lee (Journal of American Chemical Society, vol. 127, pp. 9996-9997, Jul. 2005) claimed that hydrogen is enclathrated in the CO2 hydrate. In the present study, the cage unoccupancy of hydrogen in the CO2 hydrate was reconfirmed clearly by in situ Raman spectroscopy for single crystal of gas hydrates. Isothermal phase equilibria (pressure - composition) and Raman spectra for three ternary systems of hydrogen + hydrocarbon (ethane, cyclopropane, propane) +water with same experimental procedures as hydrogen + CO2 + water system were measured at 276.1 K in the pressure range up to 5 MPa. In addition, the released gas from hydrates was analyzed to confirm the occupancy or unoccupancy ofhydrogen at the temperature. All analyses arrive at the single conclusion that hydrogen is enclathrated in only propane hydrate under the present experimental conditions.