Ready-to-use compositions for bleaching human keratin fibers, such as hair, comprising i) at least one anhydrous bleaching composition, in paste form, comprising at least one peroxygenated salt, at least one alkaline agent and from 1% to 35% by weight of at least one inert organic liquid, and ii) at least one oil-in-water emulsion comprising at least one first surfactant chosen from nonionic and anionic surfactants and at least one copolymer comprising (a) at least one unit derived from a salified or non-salified (meth)acrylic acid and (b) at least one unit derived from esters of (meth)acrylic acid and at least one first fatty alcohol chosen from saturated and unsaturated, linear and branched, ethoxylated C.sub.8-C.sub.30 fatty alcohols, wherein said ingredients (i) and (ii) are mixed before use; process for preparing the compositions; process for bleaching human keratin fibers using the compositions; and multicompartment devices comprising the compositions.