A new model has been developed for calculation of fluid-phase equilibria of asymmetric mixtures. This local-composition model extends the quasi-chemical theory of Guggenheim (known to correlate well liquid-state activity coefficients) to fluids of all densities. The model can be applied to any equation of state, contains only one new adjustable parameter per binary pair, and can be extended to multicomponent mixtures of large and small molecules by use of the surface areas of the molecules. Although the local-composition model is a nonrandomness approach, all randomness boundary conditions are met. Significant improvement over the random-mixing model is shown for the prediction of vapor-liquid equilibria of methane/water and ethane/water systems.