The invention relates to a composite structure (11) formed by a plurality of layers (13, 15, 17, 19, 21, 23) including an optical fiber (25) for structural monitoring purposes which is at least partly embedded in said structure (11), incorporating a protective cover (27) in those areas of its embedded part susceptible to needing repair, and to a process for repairing said embedded optical fiber comprising the following steps: identifying the optical fiber area in need of repair, removing material until reaching the cover (27), extracting said area, removing the protective cover (27), repairing the optical fiber (25), relocating the repaired area in the structure and returning the removed material.