Suitable pressures and temperatures for methane hydrate are found over most of the seafloor but thermodynamic equilibrium imposes an additional condition on the concentration of dissolved gas. We quantify the thermodynamic conditions for hydrate stability using a simulated annealing algorithm to minimize the free energy of a mixture of methane gas and seawater. The equilibrium state includes a description of the composition of all stable phases as a function of pressure, temperature, and salinity. When the hydrate phase is stable, we find that the equilibrium concentration of dissolved gas (solubility) decreases sharply with temperature. The gas solubility is also lowered for typical values of salinity in seawater. Since lower solubilities reduce the amount of gas required to form hydrate, the presence of salts in seawater can actually promote hydrate formation. Changes in salinity that accompany hydrate formation add a thermodynamic degree of freedom, which permits a three-phase zone to develop, where hydrate, seawater, and free gas coexist over a range of temperatures at a constant pressure. We apply our calculations to determine the location of stable phases in the seafloor. The calculated profile of gas solubility permits hydrate to crystallize directly from dissolved gas in seawater. Diffusion of gas along the gradient in the equilibrium concentration implies a continual transport of gas through the hydrate layer into the overlying ocean. In order to maintain hydrate in the seafloor sediments, a persistant source of methane is required to overcome the losses due to diffusion. Rates of hydrate growth and loss are estimated using simple models of physical conditions in marine sediments. ¿ 1998 American Geophysical Union