This paper is devoted to the solubility of mixed gases in a liquid, the goal being to predict their solubilities from binary data. Only sparingly soluble and weakly interacting gases are considered. On the basis of the Kirkwood-Buff theory of solution, two transcendental equations are derived that allow one to predict the solubility of binary mixed gases from the solubilities of pure individual gases. The suggested method was tested for the solubilities of methane-ethane, methane-n-butane, and methane-carbon dioxide gas mixtures in water at high pressures. Good agreement between experiment and predictions was found.