The invention relates to compositions for the oxidative or non-oxidative dyeing of keratin fibers, compositions for the simultaneously lightening and coloring of keratin fibers or compositions for the bleaching of keratin fibers, comprising an anionic acrylic thickener obtained by polymerization of (i) 5 to 95 molar percent of at least one monomer performing a weak acid function, and of (ii) 5 to 95 molar percent of at least one monomer performing a strong acid function, wherein such composition exhibits a fraction of water-soluble polymers ranging from 5 to 50 percent by weight of the total polymer, as well as the use of the above anionic acrylic thickener to thicken compositions for the oxidative or non-oxidative dyeing of keratin fibers, compositions for the simultaneously lightening and coloring of keratin fibers or compositions for the bleaching of keratin fibers.