AbstractHemoglobin (Hb) in solution is capable of transporting oxygen and could thus be considered as an ideal red cell substitute. However, it presents two important drawbacks : a short vascular retention time and a high oxygen affinity. Chemical modifications of Hb by polymeric reagents could overcome these limitations, but generally, polymer‐linked Hb exhibits too high an oxygen affinity. Covalent coupling of monomethoxypolyoxyethylene with Hb in conditions where the amines, essential for oxygen transport, are protected, gives rise to conjugates with good oxygen‐binding propert