Rapid arterial O(2) desaturation during apnea in the preterm infant has obvious clinical implications but to date no adequate explanation for why it exists. Understanding the factors influencing the rate of arterial O(2) desaturation during apnea (Sa(O)xe2x82x82) is complicated by the non-linear O(2) dissociation curve, falling pulmonary O(2) uptake, and by the fact that O(2) desaturation is biphasic, exhibiting a rapid phase (stage 1) followed by a slower phase when severe desaturation develops (stage 2). Using a mathematical model incorporating pulmonary uptake dynamics, we found that elevated metabolic O(2) consumption accelerates Sa(O)xe2x82x82throughout the entire desaturation process. By contrast, the remaining factors have a restricted temporal influence: low pre-apneic alveolar P(O)xe2x82x82causes an early onset of desaturation, but thereafter has little impact, reduced lung volume, hemoglobin content or cardiac output, accelerates Sa(O)xe2x82x82during stage 1, and finally, total blood O(2) capacity (blood volume and hemoglobin content) alone determines Sa(O)xe2x82x82during stage 2. Preterm infants with elevated metabolic rate, respiratory depression, low lung volume, impaired cardiac reserve, anemia, or hypovolemia, are at risk for rapid and profound apneic hypoxemia. Our insights provide a basic physiological framework that may guide clinical interpretation and design of interventions for preventing sudden apneic hypoxemia.