The disordered La0.5Ba0.5CoO3-δ ↔ ordered LaBaCo2O6-δ transition was studied in detail using several complementary in situ (X-ray diffraction, thermogravimetry, and coulometric titration) and ex situ (transmission electron microscopy) techniques. This transition was found to proceed through the formation of complex domain textured intermediate products. They were shown to have strong affinity to oxygen and exhibit its fast absorption from ambient atmosphere (oxygen partial pressure ( pO2) 0.21 atm) at a temperature as low as 70 °C. The thermodynamic stability limits of the cubic and double perovskites were determined by coulometric titration. The stability diagram of the LaBaCo2O6-δ - La0.5Ba0.5CoO3-δ system was plotted as a result. Oxygen nonstoichiometry of the thermodynamically stable cubic perovskite La0.5Ba0.5CoO3-δ was measured as a function of pO2 in the temperature range between 1000 and 1100 °C using a coulometric titration technique.