The chemical reactions leading to the decomposition of superconducting YBa2Cu3O7-x (0 > x > 0.05) in water solution and water vapor at different temperatures were investigated and the corrosion products were characterized using X-ray diffraction and scanning electron microscopy. Although the YBa2Cu3O7-x phase is stable in some nonaqueous solvents, it reacts readily with water, acids, carbon dioxide, and carbon monoxide. Samples of YBa2Cu3O7-x soaked in water solution at 25, 50, and 75-degrees-C all produce BaCO3 and CuO corrosion products as determined by X-ray powder diffraction studies. Although there is some evidence for the formation of small amounts of Y2BaCuO5 and Y2O3, the majority of the Y-containing corrosion products are produced as amorphous phases. Our studies suggest that "Y2BaCuO5" is formed with a metastable or distorted structure. Moreover, when YBa2Cu3O7-x was exposed to water vapor equilibrated at a temperature of 75-degrees-C, BaCO3 forms and increases in amount with exposure time. On the other hand, CuO and "Y2BaCuO5" form only in the initial stages of corrosion. For comparison, superconducting Tl2Ba2Ca2Cu3O10+x was also investigated, and similar results were obtained. Details related to the corrosion of these two high-T(c) phases are discussed herein.