In this paper we develop a crossover modification of the statistical associating fluid theory (SAFT) equation of state for macromolecular chain fluids which incorporates the scaling laws asymptotically close to the critical point and. is transformed into the original classical SAFT equation of state far away from the critical point. A comparison is made with experimental data for pure methane, ethane, n-hexane, n-decane, and n-eicosane in the one- and two-phase regions. We also present comparisons with experimental single-phase data for n-triacontane and n-tetracontane. We show that, over a wide range of states, the crossover SAFT model yields a much better representation of the thermodynamic properties of pure fluids than the original SAFT equation of state, The crossover SAFT equation of state reproduces the saturated pressure data in the entire temperature range from the triple point to the critical temperature with an average absolute deviation (AAD) of about 3.8%, the saturated liquid densities with an AAD of about 1.5%, and the saturated vapor densities with an AAD of about 3.4%. In the one-phase region, the crossover SAFT equation represents the experimental values of pressure in the critical region with an AAD of about 2.9% in the region bounded by 0.05 rho(c) less than or equal to rho less than or equal to 2.5 rho(c) and T-c less than or equal to T less than or equal to 2T(c), and the liquid density data with an AAD of about 3% at the pressures up to P = 2000 bar. For the n-alkanes CmH2m+2 with the molecular weight M-w > 142 (m > 10), the crossover SAFT model contains no adjustable parameters and can be used for the pure prediction of the fluid thermodynamic surface.