A method for extracorporeal elimination of one or more components from blood where whole blood or blood plasma is added to a blood treatment device containing an adsorbent which binds the one or more components is disclosed. The adsorbent comprises at least one matrix to which at least one ligand having specific binding affinity to said one or more component is covalently bound. The ligand comprises a glycosidically bound aglycon and at least one saccharide, preferably blood group determinant A, blood group determinant B, blood group H determinant, a P antigen, or a Pk antigen； or said ligand is an amino acid, a peptide or an antibody. Methods for treatment of transplant recipients, and to use a blood treatment device is also disclosed.
