Two infants, both born before term, were found apneic, cyanotic and limp at home when they were 9 weeks and 2 weeks old, respectively. Their respiration was monitored in the hospital and found to be remarkably periodic during sleep, and was in one case accompanied by pronounced bradycardia. The periodic breathing and apnea seemed to be caused by a decreased oxygen tension which can induce an instability of the central respiratory control mechanisms.