The solid state galvanic cells Pt, YBa2Cu3O7-x//(Y2O3)ZrO2//O2(1 atm), Pt and Pt, YBa2Cu4O8+Y2Ba4Cu7O14.5-y+CuO//(Y2O3)ZrO2/O2(1 atm), Pt have been employed for the measurement of limiting oxygen potentials for the decomposition of YBa2Cu3O7-x and YBa2Cu4O8 between 850 and 1100 K. The oxygen potential corresponding to the decomposition of YBa2Cu3O7-x has been calculated from the measured open-circuit voltage of the first cell at a fixed temperature after coulometrically titrating oxygen through the (Y2O3)ZrO2 solid electrolyte tube. The oxygen was titrated in both reduction and oxidation cycles. The existence of a multiphase equilibrium at a fixed temperature is indicated by a plateau on the plot of EMF versus charge transferred through the cell. The oxygen potentials for the decomposition of YBa2Cu3O7-x computed from the measured EMF can be represented by the expression Delta mu (O)2=-302200+195.7T(+or-1000)J mol-1. The equilibrium oxygen potential for the decomposition of YBa2Cu4O8 obtained from the measured EMF of the second cell is given by the expression Delta mu (O)2=-250515+222.34T(+or-1000)J mol-1.