Thermodynamic modeling is performed for the (\mathrm{Ba}-\mathrm{Cu}-\mathrm{O}) system, which is essential to a good understanding of phase and chemical equilibria in the (\mathbf{Y}-\mathrm{Ba}-\mathrm{Cu}-\mathrm{O}) and some other oxide systems containing high-temperature superconductors. A self-consistent set of thermodynamic functions of the phases (\mathrm{BaO}{2}, \mathrm{BaCu}{2} \mathrm{O}{2}), (\mathrm{BaCuO}{2}, \mathrm{Ba}{2} \mathrm{Cu}{3} \mathrm{O}{5+y}), and (\mathrm{Ba}{2} \mathrm{CuO}{3+q}) is obtained. A variety of phase equilibria in the (\mathrm{Ba}-\mathrm{Cu}-\mathrm{O}) system are calculated for a wide range of oxygen pressures and temperatures. The present thermodynamic data can be readily used for computing the phase equilibria and conditions for thermodynamic stability of oxide superconductors. It is detected that both (\mathrm{BaCuO}{2}) and (\mathrm{Ba}{2} \mathrm{CuO}{3+q}) have two stability boundaries, one at low temperatures and high oxygen pressures, and the other at high temperatures and low oxygen pressures. Critical analysis of phase equilibria in the (\mathrm{Ba}-\mathrm{Cu}-\mathrm{O}) system makes it possible to explain a number of conflicting results encountered in the literature. These contradictions arise from solid state reactions between phases, which may be very slow due to kinetic problems. O 1994 Academic Press, Inc.