A process for the continuous pretreatment of cellulosic textile material comprises PA1 a) a precleaning step wherein the treatment bath used comprises customary surfactants and other customary auxiliaries with or without customary enzymes as desizing agents and has a pH of from 5 to 11, and, after washoff and rinse, PA1 b) a bleaching step with hydrogen peroxide in an alkaline-aqueous liquor which comprises customary surfactants and other customary auxiliaries, PAL wherefor the treatment bath of (a) additionally comprises from 1 to 10% by weight, based on the weight of the textile material, PA1 (i) either of an aminopolycarboxylic acid, of a hydroxyalkyl- or amino-phosphonic acid, of a polycarboxylic acid, of a polyhydroxycarboxylic acid or of an inorganic polymetaphosphate, or a mixture thereof, as complexing agent for polyvalent metal ions, or PA1 (ii) of a water-soluble polymer derived from 40 to 100% by weight of monoethylenically unsaturated mono- or dicarboxylic acids or anhydrides, or a mixture thereof, and has a K value of from 8 to 80, as dispersant, or PA1 (iii) a mixture of components (i) and (ii) in a weight ratio of from 10:1 to 1:10.