Summary The ternary systems oleic acid‐stearic acid‐commercial hexane and oleic acid‐stearic acid‐acetone containing varying amounts of the three components have been equilibrated at 0°C., −10°C., −20°C., −30°C., and −40°C. From compositional data of the liquid and solid phases in equilibrium at each isotherm, ternary phase diagrams have been constructed. From these diagrams it is possible to predict the degree of separation which can be obtained with any given mixture of oleic and stearic acids, using either acetone or commercial hexane as solvent. With practical solvent ratios the phase diagrams at −20°C., −30°C., and −40°C., exhibit closed areas representing liquid phase composition. The liquid phase boundaries have been established for each isotherm investigated. The intersolubilizing effect of oleic acid on stearic acid, greater in commercial hexane than in acetone, and the possible formation of mixed crystals of oleic and stearic acid have been noted. Oleic acid of high purity can be obtained as one of the practical applications of these data.