The optimum and critical hemoglobin concentrations are determined by the oxygen demand of the tissues and several oxygen transport parameters (i.e., blood flow, arterial oxygen saturation, oxygen affinity of hemoglobin, and the critical venous oxygen pressure). Most of the oxygen transport parameters change markedly during the first weeks after birth. Oxygen consumption and cardiac output in neonates are three times those of adults on a body weight basis. Due to the high oxygen affinity of fetal hemoglobin, the oxygen unloading capacity of hemoglobin in neonates is about 50% less than in adults. From oxygen transport parameters and oxygen consumption we have calculated the optimum and the critical hemoglobin concentrations for preterm and full-term neonates during the first weeks after birth. A hemoglobin concentration of 15 g/dl appears optimal for preterm and full-term infants at birth as well as for adults. The calculated minimum acceptable hemoglobin concentration is 6 g/dl for children and adults, 12 g/dl for preterm infants and 11 g/dl for full-term neonates at birth. Due to the postnatal decrease in oxygen affinity, the minimum acceptable hemoglobin concentration decreases by approximately 1 g/dl/week for the first 5-6 weeks until the minimum value of 6 g/dl for children and adults is reached. The minimum hemoglobin concentration should be 2 g/dl higher in patients who require increased oxygen or suffer from other serious disorders. A minimum hemoglobin concentration of 10 g/dl is recommended in children with leukemia or other oncological disease. In infants and children with chronic hypoxemia (cyanotic congenital heart disease) the minimum hemoglobin concentration should be increased by the percentage of arterial oxygen desaturation.