Abstract: A process for delignifying and bleaching lignocellulose-containing pulp, in which the pulp is delignified with a peracid or a salt thereof, treated with a complexing agent, and subsequently bleached with a chlorine-free bleaching agent. Suitably delignification is carried out with the strongly oxidizing peracetic acid, giving a considerable increase in brightness and a considerable reduction of the kappa number after bleaching with a chlorine-free bleaching agent comprising at least one of a peroxide-containing compound, ozone or sodium dithionite, or optional sequences or mixtures thereof. The brightness increasing effect is highly selective, i.e. the viscosity of the pulp is maintained to a comparatively great extent. Both the delignification and the treatment with a complexing agent are advantageously carried out at a close to neutral pH, thus minimizing the need of pH adjustment and making it possible to use spent bleach liquor internally, e.g. for washing the pulp.