A new local composition model with two adjustable parameters per binary can represent binary vapour-liquid equilibria with good accuracy. For a ternary mixture the model includes six binary parameters and three additional ternary parameters in order to fit the model to ternary liquid-liquid equilibria. An extended form of the model for a quaternary mixture is proposed to involve further four quaternary parameters. Calculated liquid-liquid equilibrium results for 12 quaternary systems apparently show the good performance of the new model.