In an effort to synthesize monophasic superconducting oxides in the quaternary system Bi2O3-SrO-CaO-CuO two studies have been conducted. The melting relations of superconducting oxides Bi2Sr2CaCu2O8 (Bi-2212) and Bi2Sr2Ca2Cu3O10 (Bi-2223) have been experimentally investigated separately at various oxygen fugacities {f(O2)} from I to 3. 10-4 bar at 1 atm total pressure. Several interesting properties of the system have been found with respect to this portion of the quaternary; the modal proportions of liquid produced at the solidus depend on the oxygen fugacity. The amount of liquid produced at the Bi-2212 solidus reached a maximum of approximately 75% at f(O2) = 0.1 bar, Bi-2223's maximum proportion of liquid formed at the solidus continues to increase up to the lowest oxygen fugacity f(O2) = 0.01 bar studied. CaO (with a small amount of dissolved SrO) is the liquidus phase over the entire range of f(O2) for both compositions. (Sr,Ca)2CuO3 is the second phase to crystallize at high f(O2) but, as f(O2) decreases, its primary phase volume shifts for Bi-2212, and Bi2(Ca,Sr)3O6 is the second phase to form. (Sr,Ca)14Cu24O41 exhibited liquidus relationship only in high oxygen fugacities. Only Bi-2212 melts to assemblages that include bismuth-bearing crystalline phases. Bi9(Ca,Sr)16Ox is stable only at high oxygen fugacities and Bi2(Ca,Sr)3O6 is only stable at the lower values. At the lowest oxygen fugacities, Bi-2212 liquids crystallize (SrCa)CuO2 at a higher temperature than (SrCa)2CuO3 and no (Sr,Ca)CuO2 was found in Bi-2223 bulk compositions. These variations apply constraints on the positions of the univariant and invariant phase equilibria and these constraints are described.