Abstract The reduction isobar T vs δ ( pO 2 = 0.21 atm) of BaBiO 3-δ between 750 and 1050°C shows a trend with three near linear sections in the ranges 750-850°C, 850-1000°C, and 1000-1045°C, respectively. The quenching in liquid N 2 of first-section solids (phase I) does not prevent the transformations Fm3̄ m → R3̄ → I2/ m typical of the stoichiometric compound and their XRD patterns at room temperature are not different from that of the stoichiometric BaBiO 3. The quenching of the cubic structure Pm3̄ m of solids in the second section (phase II) still originates a monoclinic structure, but one strongly perturbed by the high concentration of oxygen vacancies. As already pointed out by other authors, by neutron diffraction at high temperatures, the phase II to phase III transition (third section of the isobar) occurs, unusually, in a gradual way and it is nearly complete about the melting temperature (1045°C). The close resemblance of the XRD patterns of the terms of the Aurivillius series with those of BaBiO 2.56 (phase III) leads us to think that this last phase is the term limit of the above series. Its structure would therefore be characterized by a random distribution of Ba and Bi ions in the perovskite A and B sites. The reduction of BaBiO 3 in high purity N 2 ( pO 2 ≈ 10 -6 atm) yields the polymorphous solid BaBiO 2.50. At 1000°C it still shows a structure with the tetragonal symmetry of phase III. Between 1000 and 800°C this bright red solid shows a pseudocubic perovskite-type structure, while for lower temperatures it assumes a bright yellow color and a structure with monoclinic no-longer-perovskite-type symmetry. The equilibria between the solids of the examined system were also studied through annealing and quenching in water of solids with δ = 0.2, 0.3, and 0.44, sealed in silica glass tubes. The results agree with the diagram already published by Beyerlein et al, (R. A. Beyerlein, A. J. Jacobson, and L. N. Yacullo, Mater. Res. Bull. 20, 877 (1985)) only for T values higher than 700°C. The eutectoid decomposition of phase II (δ = 0.2) to phase I and phase III (at T = 668 ± 2°C) and the subsequent decomposition of phase III to phase I plus the yellow phase BaBiO 2.5 (at 663 ± 2°C) disagrees, on the contrary, with the results of the above authors. The results of the simultaneous DTA, TG, and DTG analyses on the stoichiometric BaBiO 3 at pO 2 = 0.21 and 1 atm leads us to think that monophasic region II ( Pm3̄ m) for adequate p O 2 ( pO 2 > 1 atm) extends as far as the stoichiometric solid itself (δ = 0).