In this work, we extend the pure fluid crossover statistical associating fluid theory (HRX-SAFT) equation of state (EOS) (Kiselev et al., Fluid Phase Equilib. 2001, 183-184, 53) to fluid mixtures of polar and associating components. HRX-SAFT incorporates non-analytic scaling laws in the critical region and is transformed into the analytical, classical HR-SAFT EOS far away from the critical point. Pure CO2, H2O, and CH3OH are modeled as associating chain molecules with two association sites (i.e., model 2B). For all three pure substances, the HRX-SAFT EOS reproduces the vapor pressure data from the triple point to the critical temperature with an average absolute deviation (AAD) of about 1%, the saturated liquid and vapor densities with an AAD of about 1-3%, and the single-phase pressures in the one-phase region with an AAD of about 2-3%. Using classical composition-dependent mixing rules, we have also applied the HRX-SAFT EOS to binary mixtures. For the non-association terms in the classical HR-SAFT, we used the vdW1 mixing rules with one constant binary interaction parameter (k(ij)). For the mixture association term, we assumed that there is cross association between the carbon dioxide oxygens and the hydrogens in methanol and water. The HRX-SAFT mixture model was tested against extensive experimental data for VLE, PVTx, and excess properties in carbon dioxide + water, carbon dioxide + methanol, and water + methanol mixtures.