The disordered La0.5Ba0.5CoO3- delta <-> ordered LaBa-Co2O6-delta 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 (pO(2)) 0.21 atm) at a temperature as low as 70 degrees C. The thermodynamic stability limits of the cubic and double perovskites were determined by coulometric titration. The stability diagram of the LaBaCo2O6-delta - La0.5Ba0.5CoO3- delta system was plotted as a result. Oxygen nonstoichiometry of the thermodynamically stable cubic perovskite La0.5Ba0.5CoO3- delta was measured as a function of pO(2) in the temperature range between 1000 and 1100 degrees C using a coulometric titration technique.