We measured the thermodynamic stability conditions for the N-2, CO2, or CH4 semiclathrate hydrate formed from the aqueous solution of tri-n-butylphosphine oxide (TBPO) at 26 wt %, corresponding to the stoichiometric composition for TBPO center dot 34 center dot 5H(2)O. The measurements were performed in the temperature range 283.71-300.34 K and pressure range 0.35-19.43 MPa with the use of an isochoric equilibrium step-heating pressure-search method. The results showed that the presence of TBPO made these semiclathrate hydrates much more stable than the corresponding pure N-2, CO2, and CH, hydrates. At a given temperature, the semiclathrate hydrate of 26 wt % TB PO solution + CH4 was more stable than that of 26 wt % TBPO solution + CO2, which in turn was more stable than that of 26 wt % TBPO solution + N-2. We analyzed the phase equilibrium data using the Clausius-Clapeyron equation and found that, in the pressure range 0-20 MPa, the mean dissociation enthalpies for the semiclathrate hydrate systems of 26 wt % TBPO solution + N-2, 26 wt % TBPO solution + CO2, and 26 wt % TBPO solution + CH4 were 177.75, 206.23, and 159.00 kJ.mol(-1), respectively.