An extended law of corresponding states, in combination with a parametric crossover equation of state, is applied to the prediction of thermodynamic properties and phase behavior of pure fluids and binary mixtures over a wide region around vapor-liquid critical points. For pure fluids, a generalized form of the model is given that requires only the acentric factor of the pure component. For mixtures, the critical locus is also required. A good representation of thermodynamic property data is achieved in the range of temperatures 0.8 T-c(x) less than or equal to T less than or equal to 1.5 T-c(x) and densities 0.35 rho(c)(x) less than or equal to rho less than or equal to 1.65 rho(c)(x). Published by Elsevier Science B.V.