We have recently proposed an accurate version of the cubic-plus-association (CPA) equation of state (EOS) for water-containing mixtures which combines the Peng-Robinson equation (PR) for the physical interactions and the thermodynamic perturbation theory for the hydrogen bonding of water molecules. Despite the significant improvement, the water composition in the nonaqueous phase is systematically, underestimated for some systems where the nonwater species are methane and ethane at very high pressures, unsaturated hydrocarbons, CO2, and H2S. We attribute the deficiency to the neglect of the "cross association" between water and those nonwater molecules. In this work, the accuracy is drastically improved by treating methane, ethane, unsaturated hydrocarbons, CO2 and H2S as "pseudo-associating" components and describing the cross association with water in the framework of the perturbation theory. It is shown that the cross association is more significant for the nonaqueous phase. In addition to binary mixtures, reliable predictions are achieved for H2O/C-1/CO2/H2S quaternary mixture in two and three phases. (C) 2009 American Institute of Chemical Engineers AIChE J, 55: 1803-1813, 2009