A new chemical model is presented that permits the calculation of the excess functions and of the phase equilibrium for binary systems with one associating component. The chemical equilibrium between the associated species is described on the base of continuous thermodynamics. Therefore, the model is abbreviated by CONTAS (continuous thermodynamics of associating systems). Mostly, only three parameters for each binary system have to be fitted to experimental data. Two further parameters describing the temperature dependence of the association constant are specific for the associating component. The model is applied to 15 systems of the type non-polar component A + associating component B where, the associating components are methanol, ethanol, aniline and water. Based on the same set of parameters the excess Gibbs energy, the excess enthalpy, the vapor-liquid equilibrium and the liquid-liquid equilibrium (if there is one) are calculated. In all cases the results are reasonably well. (c) 2007 Elsevier B.V. All rights reserved.