The stabilities of Al2O3-Fe2O3-mono (AFm) and -tri (AFt) phases in the Ca-Al-S-O-H system at 25 degrees C are examined using Gibbs energy minimization as implemented by GEM-Selektor software coupled with the Nagra/PSI thermodynamic database. Equilibrium phase diagrams are constructed and compared to those reported in previous studies. The sensitivity of the calculations to the assumed solid solubility products, highlighted by the example of hydrogarnet, is likely the reason that some studies, including this one, predict a stable SO4-rich AFm phase while others do not. The majority of the effort is given for calculating the influences on AFm and AFt stability of alkali and carbonate components, both of which are typically present in cementitious binders. Higher alkali content shifts the equilibria of both AFt and AFm to lower Ca but higher Al and S concentrations in solution. More importantly, higher alkali content significantly expands the range of solution compositions in equilibrium with AFm. The introduction of carbonates alters not only the stable AFm solid solution compositions, as expected, but also influences the range of solution pH over which SO4-rich and OH-rich AFm phases are dominant. Some experimental tests are suggested that could provide validation of these calculations, which are all the more important because of the implications for resistance of portland cement binders to external sulfate attack.