An association model recently introduced by the author [D. Browarzik, Fluid Phase Equilibr. 217 (2004) 125-135] is modified and applied to more systems including aqueous systems. The model is based on chemical theory, on a G(E)-expression and on continuous thermodynamics and, is focused to the simultaneous description of liquid-liquid equilibrium (LLE) and vapor-liquid equilibrium (VLE). There is an improved calculation of the vapor pressure of the hypothetical pure associates. Furthermore, the calculation of the segment numbers in this version is based on van der Waals volumes. The model permits phase-equilibrium calculations of binary systems consisting of an associating and a non-associating component. The associating component is considered to be a mixture of associates with the composition described by a continuous distribution function that depends on temperature and on one of the mole fractions of the binary system. The equilibrium constant of association is fitted to vapor-pressure data of the associating components. The model needs only one interaction parameter depending on temperature. The accuracy of the simultaneous description of LLE and VLE is reasonably well. The systems considered are: n-pentane + methanol, n-hexane + methanol, n-heptane + methanol, n-octane + methanol, carbon disulfide + methanol, n-hexane + ethanol (VLE only), hexadecane + ethanol, 2-butanone + water, tetrahydrofuran + water. © 2004 Elsevier B.V. All rights reserved.