Water-soluble graft polymers of monosaccharides, oligosaccharides, polysaccharides and derivatives thereof, obtainable by free radical polymerization ofA) a monomer selected from, or a monomer mixture of,(a) from 20 to 100% by weight of acrylic acid or methacrylic acid or of a mixture thereof or of the alkali metal, alkaline earth metal or ammonium salts thereof,(b) from 0 to 80% by weight of other monoethylenically unsaturated monomers which are copolymerizable with the monomers (a) and(c) from 0 to 5% by weight of monomers having at least 2 ethylenically unsaturated, nonconjugated double bonds in the molecule,in the presence ofB) monosaccharides, oligosaccharides, polysaccharides, oxidatively, hydrolyrically or enzymatically degraded polysaccharides, oxidized hydrolyrically degraded or oxidized enzymatically degraded polysaccharides, chemically modified mono-, oligo- or polysaccharides or a mixture of the stated compounds in a weight ratio A:B of from 95:5 to 20:80, are used as a tanning agent for the self-tanning, pretanning and simultaneous tanning of pelts and skins and for the retanning of leather and skin.