High-temperature phase stability limits of TlCaBaCuO superconductors were determined as a function of Tl 2O partial pressure at constant O 2 partial pressure (≈630 Torr), sample temperature (880°C), and sample Ca:Ba:Cu ratio (1:2:2, 2:2:3, and 3:2:4). Both phases with double CuO 2 sheets in the structure, 2122 and 1122, were stable over wide ranges of P(Tl 2O) for stoichiometric (1:2:2) samples. At relatively high P(Tl 2O), 2122 was also the stable superconducting phase even for the Ca-and Cu-rich stoichiometries. Energy-dispersive X-ray spectra and c-axis differences suggested variable cation stoichiometry in 1122 and 2122 prepared under such a range of conditions. However, the superconducting transition temperatures and a-axes of both 1122 and 2122 were nearly constant for all conditions of preparation, suggesting a nearly constant carrier density. No range of P(Tl 2O) was found where either 1223 or 2223 was stable as a single superconducting phase for the P(O 2) and temperature employed. Intergrown mixtures of 1223 and 2223 or Tl-free phases were found when P(Tl 2O) was below the 2122 formation boundary.