We extend the Statistical Associating Fluid Theory, SAFT, to vapour-liquid equilibria of fluid mixtures in which all components hydrogen bond. We refit parameters for carbon dioxide and water to obtain better agreement with experiment, and more consistency with parameters for other associating molecules. For monoethanolamine and diethanolamine, we obtain deviations in the individual mole fractions of 1 to 2% between the SAFT predictions and the smoothed experimental data. For aqueous mixtures we determine values of the single temperature-independent binary parameters, and then use these parameters to predict phase equilibria of ternary aqueous mixtures of monoethanolamine or diethanolamine with carbon dioxide. Our results deviate an average of 0.01 in mole fraction units from the experimental mole fractions. The SAFT equation slightly overpredicts the amount of alkanolamine, and underpredicts the amount of carbon dioxide in the liquid mixture. Small deviations in the liquid mole fraction produce large deviations in the carbon dioxide loading ratio, the ratio of moles of carbon dioxide to moles of alkanolamine in the liquid, giving average deviations of 43%.