This report is based on a study of 53 infants, 28 of whom had clinically observed prolonged apnea (≥ 20 seconds) during sleep whereas the remaining did not. In addition to the clinical observations, each infant was studied in a sleep laboratory during a complete nap, and a continuous recording was made of respiratory activity and rapid eye movements. Measurements were made of all apneic pauses (≥ 2 seconds) observed in the laboratory and the two groups of infants were compared in terms of the frequency and average duration of apneic pauses, the longest apneic pause, the amount of periodic apnea, and the relative amount of apnea. The infants with prolonged sleep apnea had, during a single nap, more frequent and longer apneic pauses and more periodic apnea. This supports the hypothesis that respiratory instability during sleep and prolonged apnea have a common etiology. By employing a multiple linear regression model and including all laboratory apnea measures in a single analysis, a composite laboratory score was developed to differentiate members of the two groups. It would thus appear that the study of infants during a single nap could assist in the identification of infants at risk for prolonged sleep apnea and provide an indirect method for determining the influence of a number of variables on the occurrence of prolonged sleep apnea.