The Gibbs ensemble algorithm is implemented to determine the liquid-liquid phase coexistence of binary fluid mixtures interacting via a two-body Lennard-Jones + three-body Axilrod-Teller potential. The contributions of both two-body and three-body interactions are calculated exactly. The addition of the Axilrod-Teller term can affect liquid-liquid miscibility substantially. In particular, Axilrod-Teller interactions have a large effect on the densities of the coexisting liquid phases. (C) 1998 Elsevier Science B.V. All rights reserved.