In premature infants, apnea of prematurity is one of their major clinical problems. Caffeine is currently a worldwide therapy to reduce the number and severity of these apneas. This practice has shown to be safe on cognitive and neurodevelopmental outcomes at 18 to 21 months of age. However, caffeine is not 100% effective, and may have little effect on hypoxemia and bradycardia. Infants with intractable apneas unresponsive to caffeine treatment may require endotracheal intubation and mechanical ventilation. This procedure is invasive and has been associated with complications and increased risk for chronic lung disease and adverse neurodevelopmental outcome. Therefore, an alternative treatment modality would be preferable if it would prevent the infants from requiring endotracheal intubation. The investigators have been testing the overall hypothesis that small concentrations of inhaled CO2 (~1%) are effective in treating apnea of prematurity. The investigators have completed three studies in preterm infants showing that inhalation of low concentration of CO2, in infants not on caffeine, regularize breathing and decrease apneas significantly. The effects of inhalation of CO2 in infants already on caffeine, are unknown. The hypothesis to be tested is that inhalation of low concentration CO2 (1%) will significantly reduce apnea in infants treated with caffeine. The investigators have three specific aims in this proposal. 1) the investigators want to know if the apnea rate (number of apneas of ≥5 seconds/hour) is decreased with CO2 inhalation in preterm infants already on caffeine for the treatment of apnea of prematurity; 2) the investigators want to know whether inhalation of CO2 can make breathing more regular with less apneic time and whether it decreases prolonged apneas (>20 seconds) in infants already on caffeine for the treatment of apnea of prematurity; 3) the investigators want to assess the effect of inhalation of low concentration of CO2 on the regional oxygen saturation of the brain measured by near-infrared spectroscopy (NIRS) during apneas. This is to see whether CO2, by protecting cerebral blood flow, minimizes the decrease in cerebral oxygenation during apneas. This study entails a new and possibly more physiological method of treating apneas of prematurity that can be added to the present treatment of caffeine. These two treatments together, could minimize the number and severity of apneas and possibly decrease the need for mechanical ventilation in preterm infants.