Abstract The experimental results concerning the facilitation of oxygen diffusion in the presence of hemoglobin or myoglobin may be explained by the simultaneous diffusion of oxyhemoglobin or oxymyoglobin. In order to prove this assumption it should be possible to show that there is quantitative agreement between the experimental values and those computed using the physical parameters obtained independently. The present authors previously presented an approximate solution for the basic equations of diffusion including chemical reactions; an improved solution is provided in the present paper. Since the agreement between experiments and computer solutions was much less satisfactory in the system Mb+O 2 than in the system Hb + O 2, we investigated the effects of various other factors of possible importance for both systems of Hb and Mb. These computations led to the following conclusions: 1. 1. The values of the pigment diffusion coefficients are of crucial importance; 2. 2. The knowledge of the actual diffusion path length is also important; a quantitative theoretical treatment is presented; 3. 3. Concerning the chemical reaction rates the dissociation constant is more likely to be limiting; 4. 4. The effect of a possible and even minute oxygen back pressure on the low pressure side may be crucial in the case of the system Mb + O 2; 5. 5. The nonequilibrium approach suggested here is valid more generally than the equilibrium assumption made in most previous cases; the latter is apt to provide too high computed fluxes; 6. 6. Contrary to previous presumption there is a decrease of the facilitated oxygen flux with high values of P O 2 , particularly in the system Mb + O 2. These results might provide new insight in the mechanism of facilitated oxygen diffusion and suggest more appropriate experimental arrangements in future investigations.