We have clarified the use of Wyman's differential equation for the facilitated oxygen flux through a slab of solution of myoglobin or hemoglobin by showing that there is a unique choice of boundary condition on the carrier concentration to be employed in conjunction with it. The singular perturbation solution of Wyman's equation, due to Murrayand Mitchell and Murray, has been extended. By means of it, the paradox of Wittenberg, that the facilitated oxygen flux per mole of heme is apparently independent of the protein carrier, has been resolved.