A new data treatment approach for ternary systems is presented. The method is a model-free technique based on Barker's equation and integration of the Gibbs-Duhem relation. It yields numerical information for the excess Gibbs energy and activity coefficients of a ternary system and its constituent binaries. Depending on the availability of data, the method is applicable to completely miscible isothermal or isobaric systems in vapor-liquid equilibrium, at low pressures, and is useful for selecting a GE model able to correlate accurately the data. Physical constraints for the curvature of the bubble surface in the vicinity of multicomponent azeotropic concentrations are deduced from the displacement theory. The relation of these constraints with the model-free approach is discussed.