Deliming composition for deliming hides, characterized in that the deliming composition at least comprises: - a hide for deliming; and - a deliming agent, the deliming agent comprising a graft polymer of at least one of polysaccharides, polypeptides or derivatives thereof, wherein the derivatives of the polysaccharides are oxidatively, hydrolytically or enzymatically degraded polysaccharides, oxidized hydrolytically degraded or oxidized enzymatically degraded polysaccharides or suchlike chemically modified degraded products or chemically modified mono-, oligo- or polysaccharides and wherein the derivatives of the polypeptides are hydrolytically or enzymatically degraded and optionally chemically modified polypeptides, the graft polymer being obtainable by radical polymerization of A) a monomer selected from or a monomer mixture of (a) acrylic acid or methacrylic acid or a mixture thereof or the alkali metal, alkaline earth metal or ammonium salts thereof, and optionally at least one of (b) and (c), where (b) comprise monoethylenically unsaturated monomers other than the monomers (a) and copolymerizable with the monomer (a), and where (c) comprise monomers having at least two ethylenically unsaturated, nonconjugated double bonds in the molecule, in the presence of at least one of B1) polysaccharides, oxidatively, hydrolytically or enzymatically degraded polysaccharides, oxidized hydrolytically degraded or oxidized enzymatically degraded polysaccharides or suchlike chemically modified degraded products, chemically modified mono-, oligo- or polysaccharides, or mixtures of the specified compounds, and B2) polypeptides, hydrolytically or enzymatically degraded and optionally chemically modified polypeptides, or mixtures of the specified compounds. - a hide for deliming; and - a deliming agent, the deliming agent comprising a graft polymer of at least one of polysaccharides, polypeptides or derivatives thereof, wherein the derivatives of the polysaccharides are oxidatively, hydrolytically or enzymatically degraded polysaccharides, oxidized hydrolytically degraded or oxidized enzymatically degraded polysaccharides or suchlike chemically modified degraded products or chemically modified mono-, oligo- or polysaccharides and wherein the derivatives of the polypeptides are hydrolytically or enzymatically degraded and optionally chemically modified polypeptides, the graft polymer being obtainable by radical polymerization of A) a monomer selected from or a monomer mixture of (a) acrylic acid or methacrylic acid or a mixture thereof or the alkali metal, alkaline earth metal or ammonium salts thereof, and optionally at least one of (b) and (c), where (b) comprise monoethylenically unsaturated monomers other than the monomers (a) and copolymerizable with the monomer (a), and where (c) comprise monomers having at least two ethylenically unsaturated, nonconjugated double bonds in the molecule, in the presence of at least one of B1) polysaccharides, oxidatively, hydrolytically or enzymatically degraded polysaccharides, oxidized hydrolytically degraded or oxidized enzymatically degraded polysaccharides or suchlike chemically modified degraded products, chemically modified mono-, oligo- or polysaccharides, or mixtures of the specified compounds, and B2) polypeptides, hydrolytically or enzymatically degraded and optionally chemically modified polypeptides, or mixtures of the specified compounds. a graft polymer of at least one of polysaccharides, polypeptides or derivatives thereof, wherein the derivatives of the polysaccharides are oxidatively, hydrolytically or enzymatically degraded polysaccharides, oxidized hydrolytically degraded or oxidized enzymatically degraded polysaccharides or suchlike chemically modified degraded products or chemically modified mono-, oligo- or polysaccharides and wherein the derivatives of the polypeptides are hydrolytically or enzymatically degraded and optionally chemically modified polypeptides, the graft polymer being obtainable by radical polymerization of A) a monomer selected from or a monomer mixture of (a) acrylic acid or methacrylic acid or a mixture thereof or the alkali metal, alkaline earth metal or ammonium salts thereof, and optionally at least one of (b) and (c), where (b) comprise monoethylenically unsaturated monomers other than the monomers (a) and copolymerizable with the monomer (a), and where (c) comprise monomers having at least two ethylenically unsaturated, nonconjugated double bonds in the molecule, in the presence of at least one of (a) acrylic acid or methacrylic acid or a mixture thereof or the alkali metal, alkaline earth metal or ammonium salts thereof, and optionally at least one of (b) and (c), where (b) comprise monoethylenically unsaturated monomers other than the monomers (a) and copolymerizable with the monomer (a), and where (c) comprise monomers having at least two ethylenically unsaturated, nonconjugated double bonds in the molecule, B1) polysaccharides, oxidatively, hydrolytically or enzymatically degraded polysaccharides, oxidized hydrolytically degraded or oxidized enzymatically degraded polysaccharides or suchlike chemically modified degraded products, chemically modified mono-, oligo- or polysaccharides, or mixtures of the specified compounds, and B2) polypeptides, hydrolytically or enzymatically degraded and optionally chemically modified polypeptides, or mixtures of the specified compounds.