An apparatus for the treatment of blood or plasma by extracorporeal circulation includes a compartment for the circulation of blood. The compartment is provided with two accesses and has at least one inner surface intended to be coated, after sterilization, with at least one molecular layer of a substance soluble in an aqueous solution. The aqueous solution is capable of increasing the bicompatibility of the inner surface of the compartment. A determined quantity of the substance is deposited inside the blood compartment, at one of the accesses, in a form such that the substance is capable of undergoing, substantially without deterioration, an irradiation capable of sterilizing the apparatus. The quantity of substance is determined such that the circulation of a determined volume of aqueous solution through the blood compartment, starting from the access where the substance has been deposited, should result in the formation, by durable bonding, of at least one molecular layer of the substance on the inner surface of the blood compartment to be treated.