Infants enrolled in this research study will be randomized to in hospital observation versus early discharge home with caffeine and a home monitor. Neither strategy is experimental as both are currently utilized by neonatologists locally and nationally. A direct comparison of the two treatments, however, has never been undertaken in a study. If an infant is assigned to the in hospital group, they will remain in the hospital until an apnea free period of at least 5 consecutive days has been established. Outpatient follow up will occur per unit standard and typically includes a nursing visit and a doctor visit within 2-3 days of discharge. Caregivers will be asked to complete 3 brief questionnaires at enrollment, at 1 month after hospital discharge, and at 6 months of age. Each questionnaire will ask about topics such as satisfaction with hospital stay, quality of life, and numbers of acute care visits and/or rehospitalizations. Alternatively, if an infant is assigned to the early discharge group, caffeine will be given to the infant and if after a 3 day period no further apnea is noted the infant will be discharged home with continued daily caffeine therapy by mouth as well as a home monitor. Caffeine is a very commonly used drug in neonates and has an excellent safety profile. Side effects are minimal and may infrequently consist of gastroesophageal reflux. All caregivers will receive training on the use of a home monitor. Initial outpatient follow up will occur per unit standard and typically includes a nursing visit and a doctor visit within 2-3 days of discharge. Additionally, caregivers will be contacted via telephone within 2 days to answer any questions or address any concerns pertaining to apneic events, home monitor use, or caffeine therapy. Follow up in the pulmonary clinic will be arranged at 42-43 weeks gestational age at which time caregivers will be taught to determine the baseline frequency of monitor alarms on caffeine. At 43 weeks corrected gestational age, caregivers will be instructed to discontinue caffeine therapy and advised to contact the pulmonary clinic should alarm frequency increase. An outpatient recorded oximetry study will be arranged at least 1 week after discontinuation of caffeine therapy. Home pulse oximetry monitoring will be discontinued if no significant events are recorded. Caregivers will be asked to complete 3 brief questionnaires at enrollment, at 1 month after discontinuation of the home monitor, and at 6 months of age. Each questionnaire will ask about topics such as satisfaction with hospital stay, quality of life, and numbers monitor alarms, acute care visits and/or rehospitalizations.