Fiber structures such as staple fibers, filaments, yarns as well as textile sheet structures such as woven or knitted fabrics as well as non-woven fabrics and the like made from multicomponent fibers of the matrix-segment type having in their cross sections a plurality of segments arranged peripherally without being fully surrounded by the matrix and being composed of polyalkylene terephthalate and copolyamides based on .epsilon.-caprolactam and hexamethylene diamine/adipic acid salt, are split by treatment with liquid or vaporous water. The difference in shrinkage between copolyamide and polyalkylene terephthalate in water is temporarily at least 10%. Corresponding short-staple fibers are particularly well suited for making wet-laid non-woven fabrics. The water used for treatment of the fiber structures may contain inorganic salts.