A new approach is proposed to extend UNIFAC to more complex substances. While first-order solution-of-groups methods such as UNIFAC can successfully represent measured phase equilibria for structurally simple systems such as mixtures of n-alkanes and linear alkanols with good accuracy, they are not as good for branched chain and polyfunctional substances such as secondary or tertiary alcohols and diols with branched or cyclic alkanes. Our method models departure from first-order behavior by adding second-order contributions to first-order correlations. The second-order contributions are derived from perturbations with respect to structural and energetic parameters. The basis of the extension and its ability to correlate and predict effects due to structural differences in VLE, SLE, and activity coefficients at infinite dilution (gamma(infinity)) for binary and multicomponent systems is described. Addition of a few second-order group parameters to the UNIFAC tables has improved the results for essentially all cases where the molecular structure justifies including such effects.