By using published experimental values of the standard oxygen (O₂) equilibrium curve and the in vivo arterial and venous O₂ pressure (PO₂) of fetal and maternal blood in five mammalian species (human, cow, pig, sheep, and horse), we investigated the relationship between the efficiency of O₂ delivery and the effectiveness of the Bohr shift, and discussed the significance of cooperativity for mammalian Hb. The O₂ delivery of fetal blood was more efficient than that of maternal blood, and the effectiveness of the Bohr shift at both O₂ loading and release sites of fetal blood was high. A linear relationship was observed between the efficiency of O₂ delivery and the effectiveness of the Bohr shift at O₂ loading sites of the five mammalian species. In both fetal and maternal blood, the theoretically obtained optimal P₅₀ value for O₂ delivery (optP_50(OD)) was nearly equal to the optimal P₅₀ value for the effectiveness of the Bohr shift at the O₂ loading site (optP_{50(BS)(loading)}). This phenomenon was favorable for fetal blood to uptake O₂ from maternal blood with the aid of the Bohr shift and to deliver a large amount of O₂ to the tissues. The optP₅₀s for the effectiveness of the Bohr shift at given arterial PO₂ (P_aO₂) and venous PO₂ (P_vMO₂) were derived as follows: optP_{50(BS)(loading)} = P_aO₂((n 1)/(n-1))^1/n, and optP_{50(BS)(release)} = P_vO₂((n 1)/(n-1))^1/n. The relationship between in vivo PO₂s and n, P_aO₂/P_vO₂ = ((n 1)/(n-1))^2/n, was derived by letting optP₅₀ for the efficiency of O₂ delivery be equal to that for the effectiveness of the Bohr shift.