An olefin polymer composition comprising (ppm with respect to the polymer): a lactone of the furan-2-one type, a phenol in amounts of 50 to 200 ppm, a sterically hindered amine in amounts of 50 to 300 ppm, and an organic phosphite and/or organic phosphonite in amounts of 50 to less than 280 ppm. The polymer composition contains the unsubstituted furan-2-one moiety in amounts ranging from 11 to 49 ppm with respect to the polymer. Staple fibres with high tenacity and elongation at break and non-woven fabrics are prepared from such an olefin polymer composition.