A new chemical model is presented that permits the calculation of excess functions and phase equilibria for binary and ternary systems with one associating component. Mass action law is used to describe the equilibria between the associates. The physical interactions are expressed by the Ο-parameter of the Flory-Huggins lattice theory. The fundamental assumptions are similar to those in the previously published model CONTAS, but continuous thermodynamics is not used. For two ternary systems (3-methylpentane + ethanol + methylcyclohexane, benzene + ethanol + carbon tetrachloride) the vapour-liquid equilibrium, and for two other ternary systems (n-heptane + methanol + n-hexane, n-heptane + methanol + benzene) the liquidliquid equilibrium is predicted. There is a good agreement of the predicted data with the experimental ones. The calculations are only based on the association constants of the alcohols and on the interaction parameters of the binary subsystems fitted to binary experimental data. For all binary subsystems excess Gibbs energy, excess enthalpy, vapour-liquid equilibrium and liquid-liquid equilibrium (if there is one) are described reasonably well.