Initial phase equilibrium data are reported for 10 methane + liquid hydrocarbon systems forming structure H hydrates in the pressure range of 1-6 MPa. Four-phase equilibrium conditions were measured for each system, with paraffinic, naphthenic, and olefinic liquid hydrocarbons filling the large cage of structure H, and methane stabilizing the two smaller cages present in the hydrate. Many of these liquid hydrocarbons constitute a small fraction of crude oils and condensates, and the high stability and relative ease of formation of structure H suggest a possible impact of these hydrates upon hydrocarbon facilities.