A new local composition model with two adjustable parameters has been shown to be able to represent binary vapour-liquid equilibria and to predict ternary vapour-liquid equilibria with good accuracy using only binary parameters. The model has been extended to include an additional three ternary parameters per ternary in order to fit the model to ternary liquid-liquid equilibria. Calculated liquid-liquid equilibria for 19 ternary systems demonstrate clearly the better fit of the new model compared with those derived from the modified forms of the Wilson equation suggested by Hiranuma (see Nagata and Watanabe, Fluid Phase Equilibria, 72 (1992) 1-14 and Higashiuchi et al., Sekyu Gakkaishi, 33 (1990) 62-66).