diepoxide divinyl sulfone diisocyanate especially hexamethylenediisocyanate cyclohexanediisocyanate and 2 6 bisisocyanatobenzensulfonic acid di n hydroxysuccinimidyl ester diimidoester or dialdehyde particularly glyoxal the similarly reactive glycolaldehyde or glutaraldehyde these products are then linked in particular with a polyethylene glycol or with other suitable macromolecules among them for example are polyethylene oxide polypropylene oxide or a copolymer of ethylene oxide and propylene oxide or an ester ether or esteramide thereof it is also preferred for the covalently linked polyalkylene oxide to have a molecular weight of 200 to 5000 g mole the preparation of such modified oxygen binders is described in the aforementioned german patent applications and is incorporated herein very highly preferred are hyperpolymers that are prepared from deoxygenated swine hemoglobin with glutaraldehyde as the bifunctional crosslinker and polyethylene glycol as the covalently bonded macromolecule for surface modification see de 100 41 740 a1 or de 100 41 744 a1 it has been found according to the invention that hemoglobin hyperpolymers with an average degree of polymerization that is large enough for it to be able to be introduced into the blood as an artificial oxygen carrier as a therapeutic blood additive without increasing the blood volume more than slightly see above are suitable if they produce only a certain low oncotic pressure in an aqueous electrolyte solution this is related to the suitable average degree of polymerization or to the proportional molecular weight of the modified polymeric hemoglobin this involves the number average because the number of effective molecules is responsible for the oncotic pressure it has been found in particular that the.