The invention relates to a process for producing cellulose fibres comprising the steps (A) dissolving a cellulose-containing material in an aqueous tertiary amine oxide to obtain a spinnable cellulose solution; (B) spinning the cellulose solution and taking it through an aqueous precipitation bath, giving water-containing swollen filaments; (C) crushing the water-containing swollen filaments at different points so that there are at least two crushed points per millimetre of filament length, and (D) drying the crushed filaments to obtain cellulose fibres; in which the filaments are crushed under sufficient pressure so that the crushed points also remain on the dried fibre and are visible as colour changes when observed under linearly polarised light.