The experimental data on decomposition temperatures for the gas hydrates of ethane, propane, and carbon dioxide dispersed in silica gel mesopores are reported. The studies were performed at pressures up to 1 GPa. It is shown that the experimental dependence of hydrate decomposition temperature on the size of pores that limit the size of hydrate particles can be described on the basis of the Gibbs-Thomson equation only if one takes into account changes in the shape coefficient that is present in the equation; in turn, the value of this coefficient depends on a method of mesopore size determination. A mechanism of hydrate formation in mesoporous medium is proposed. Experimental data providing evidence of the possibility of the formation of hydrate compounds in hydrophobic matrixes under high pressure are reported. Decomposition temperature of those hydrate compounds is higher than that for the bulk hydrates of the corresponding gases.