The growth and stability of the (Bi1-xPbx)2Sr2Ca2Cu3Oy (Bi-2223) phase contained in silver-sheathed wires has been investigated by a combination of x-ray diffraction, scanning electron microscopy, energy dispersive x-ray analysis, and transmission electron microscopy. Silver tubes loaded with Bi-2223 precursor powders were processed into filaments using established metallurgical techniques. The filaments were then heat-treated at selected temperatures (800 to 845°C) for a range of times (10 to 6000 min) in a 7.5% oxygen atmosphere. From these studies it has been possible to investigate the time-temperature-oxygen pressure domains wherein Bi2Sr2CaCu2O8 (Bi-2212) + second phases transform to Bi-2223. Fractional conversion (Bi-2212 --> Bi-2223) versus time data show good conformance to the kinetic model for a diffusion-controlled reaction at the interface between thin sheets and a fine powder or a fluid. Quenching experiments also reveal that the Bi-2223 phase is stable in a limited temperature interval between 810 and 830°C.