Infants with prior clinical treatment with caffeine in the neonatal intensive care unit (NICU) will be enrolled and continuous physiologic data recording of oxygen hemoglobin saturation (HbO2 SAT) and heart rate will begin as early as 33 weeks postmenstrual age (PMA). Randomization will occur when enrolled infants reach a corrected gestational age of at least 34 weeks PMA AND clinical caffeine has been discontinued for at least 5 days. Infants will be randomized to receive caffeine or to continue with usual care. The group randomized to start caffeine will receive an oral loading dose of caffeine citrate of 20 mg/kg on Day #1, followed by a single daily oral maintenance dose of 6 mg/kg starting on Day #2 and continued daily thereafter until 40 weeks PMA. The continuous oximeter recordings will be stopped at the same time. The number of intermittent hypoxia events/hour per week will be compared between the caffeine group and the usual care (no-caffeine) group for each week of physiologic data recordings.