The 124 phase YBa 2Cu 4O 8 is synthesized by solid state reaction at 930°C in P(O 2)>62;30 bar, while the 247 phase Y 2Ba 4Cu 7O 15- x is favored in the narrow range of P(O 2) between 10 and 30 bar. The 123 phase YBa 2Cu 3O 7-δ forms at P(O 2)< 10 bar. Similar results are found for the rare earth analogs. The pressure ranges for stability of 123/247/124 are nearly independent of starting stoichiometry, but increase with temperature, such that the oxygen content of 123 at the phase boundary is nearly constant. This suggests that superconducting 123 (with oxygen>62;6.6) may be thermodynamically unstable to decomposition into 124 (plus non-superconducting compounds) at all temperatures, with synthesis of 124 at low temperatures and oxygen pressure limited only by kinetics. Since very high oxygen pressures are not required, synthesis of the 124 and 247 phases is relatively easy, this may have considerable practical importance.