Abstract: A new process for more easily making a superconducting matrix of YBa.sub.2 Cu.sub.3 O.sub.7-x with fine and homogeneously dispersed Y.sub.2 BaCuO.sub.5 inclusions smaller than one micron compacts powders of YBa.sub.2 Cu.sub.3 O.sub.7-x and Y.sub.2 BaCuO.sub.5 into samples which are first sintered for improved mechanical stability and then placed into contact with each other. The samples are placed into a furnace above the peritectic temperature of the YBa.sub.2 Cu.sub.3 O.sub.7-x and held at that temperature for less than about fifteen minutes so that the YBa.sub.2 Cu.sub.3 O.sub.7-x begins to melt and be absorbed by capillary action into the Y.sub.2 BaCuO.sub.5 sample. The combined sample is cooled to a temperature below the peritectic temperature by a variety of alternative cooling cycles where it is transformed by a reaction into a superconducting matrix of YBa.sub.2 Cu.sub.3 O.sub.7-x with fine and homogeneously dispersed Y.sub.2 BaCuO.sub.5. BaCuO.sub.2 +CuO may be substituted for the YBa.sub.2 Cu.sub.