Al2O3-Mo and Al2O3-W systems in a controlled Ar(95%) + H-2(5%) atmosphere at T = 2400 K and P = 1 bar have been calculated by the Monte Carlo method. It is established that the presence of hydrogen in these systems leads to the occurrence of OH, H2O2, HO2, H2O, AlOH, AlOOH, AlH, AlH2, and AlH3 components in the gas phase; aluminum hydrides are formed only through the interaction of hydrogen with melt evaporation products. The presence of reducing medium leads to a decrease in the free oxygen concentration by one to two orders of magnitude, which is expected to improve the quality of sapphire crystals.