We have developed a "global" crossover (GC) statistical associating fluid theory (SAFT) equation of state (EOS) for associating fluids that incorporates nonanalytic scaling laws in the critical region and in the limit of low densities, rho -> 0, is transformed into the ideal-gas equation EOS. Unlike the crossover SAFT EOS developed earlier, the new GC SAFT EOS contains a so-called kernel term and reproduces the asymptotic scaling behavior of the isochoric heat capacity in the one-and two-phase regions. In addition, we develop on the basis of the density functional theory (DFT) a GC SAFT-DFT model for the surface tension. In the second step, using the GC SAFT EOS and the decoupled-mode theory (DMT), we have developed a generalized GC SAFT-DMT model for transport coefficients that reproduces the singular behavior of the thermal conductivity of pure fluids in the critical region. Unlike the DMT model based on the asymptotic crossover EOS, the GC SAFT-DMT model is valid in the entire fluid state region at T >= T-b (where T-b is the binodal temperature), and at rho -> 0 reproduces the dilute gas contributions for the transport coefficients. A comparison was made with experimental data for methanol, ethanol, and higher n-alkanols. For n-alkanols, the GC SAFT-DFT/DMT model contains the same number of the adjustable parameters as the original classical SAFT EOS but reproduces with high accuracy the PVT, VLE, isochoric, and isobaric specific heats, surface tension, and thermal conductivity data close to and far from the critical point.