Thermodynamic and equilibrium swelling characteristics of three-component emulsions of polymer particles are important in producing latex systems. J. Ugelstad and P. C. Mork (Adv. Colloid Interface Sci. 13, 101, 1980) examined the thermodynamic properties of ternary systems consisting of an organic solvent, a polymer, and water. We have developed a new theoretical model which can be used to predict the equilibrium content of organic solvent in the polymer particles, when this solvent is also partially soluble in the external aqueous phase. In Part II (C. Bindschaedler, R. Gurny, E. Doelker, and N. A. Peppas, J. Colloid Interface Sci. 108, 83, 1985), this model is used to interpret the equilibrium properties of cellulose acetate emulsions.