A graft polymer of polysaccharides or polypeptides or its respective derivatives, obtainable by free radical polymerization of A) 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 of either B1) polysaccharides, oxidatively, hydrolytically or enzymatically degraded polysaccharides, oxidized hydrolytically degraded or oxidized enzymatically degraded polysaccharides, or such chemically modified degraded products, chemically modified mono-, oligo-or poly-saccharides or mixtures of the stated compounds and/or B2) polypeptides, their hydrolysates or enzymaticallydegraded and optionally chemically modified products or mixtures of the stated compounds in a weight ratio A: (B1 or B2) of from 1:99 to 18:82 or in a weight ratio A:(B1+B2) of from 60:40 to 1:99 and B1:B2 of from 97:3 to 3:97 used as tanning agents.