The dependences of the degrees of oxygen nonstoichiometry in NdzCu04_6and Nd,,,,CeO.,,CuO,_don temperature and oxygen pressure have been determined by thermogravimetric measurements in the range of temperature 350-950°C and the range of oxygen pressure 1 0m5-1 atm. The nature of the decomposition of these oxides in the range of oxygen pressure 1 0e5-1 atm has been determined by thermogravimetric analysis and X-ray diffraction. In the solid state, decreasing oxygen pressure causes Nd2Cu04_6 to decompose to NdCu02+Nd203 and then to Nd203+Cu20. The solid solution Nd1,s5Ce0.,SCu04_-d decomposes to Nd203 +NdCeOg., + CulO. The solidus line of incongruent melting has been determined in the range of oxygen partial pressure 10m6-1 atm by differential thermal analysis and the phases formed on solidification have been identified by X-ray diffraction. The phase stability diagrams for Nd2Cu04_s and Nd1.8SCe0.15Cu04_~ have been constructed. The dependence of the onset of superconductivity in Ndl.s5Ce0,,,Cu04_bon the oxygen pressure and temperature at which the specimen was annealed, and hence on the oxygen nonstoichiometry, has been determined.