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This work presents a thorough identification and analysis of the dissolution and diffusion-based reaction processes that occur during the drawing of YBa2Cu3O7−x (YBCO) glass-clad fibers, using the molten-core approach, on a fiber draw tower in vacuum and in oxygen atmospheres. The results identify the dissolution of the fused silica cladding and the subsequent diffusion of silicon and oxygen into the molten YBCO core. This leads to a phase separation due to a miscibility gap which occurs in the YBCO–SiO2 system. Due to this phase separation, silica-rich precipitations form upon quenching. XRD analyses reveal that the core of the vacuum as-drawn YBCO fiber is amorphous. Heat-treatments of the vacuum as-drawn fibers in the 800–1200 °C range show that cuprite crystallizes out of the amorphous matrix by 800 °C, followed by cristobalite by 900 °C. Heat-treatments at 1100 °C and 1200 °C lead to the formation of barium copper and yttrium barium silicates. These results provide a fundamental understanding of phase relations in the YBCO–SiO2 glass-clad system as well as indispensable insights covering general glass-clad fibers drawn using the molten-core approach.