Liquid bleaching composition components are claimed which comprise 1) amphiphilic copolymers which include structural units which are derived from a) acryloyldimethyltauric acid in free, partially neutralized or completely neutralized form with mono- or divalent inorganic or organic cations and b) at least one hydrophobic comonomer based on ethylenically unsaturated polyalkylene alkoxylates and optionally c) further at least monovinylically unsaturated comonomers different from a) and b), and 2) at least one bleach activator, bleach catalyst or oxygen transfer agent.