Based on the osmotic virial equation by McMillan and Mayer, thermodynamically consistent expressions for the Gibbs free energy of mixing and the chemical potentials of the solutes are derived. In this derivation the concentration dependence of the specific volume is accounted for explicitly. The omostic virial coefficients are determined from water-activity data in binary and ternary solutions of poly(ethylene glycol) and dextran of various molecular weights. This consistent osmotic virial equation is then tested to predict the Liquid-liquid equilibria of the ternary systems. On the basis of the parameters obtained solely from water activities the concentrations as well as the molecular-weight distributions of the polymers in the coexisting liquid phases of the aqueous two-phase systems can be predicted in goad agreement with the experimental data.