Premature infants with severe respiratory insufficiency (respiratory Group III) had more irregular respiratory rhythms and more severe apnea than healthy premature infants (respiratory Groups I and II). Birth weight did not appear to be a factor in the occurrence of severe apnea unless severe respiratory insufficiency was present. The prognosis for survival was significantly poorer among infants with severe apnea than among those who did not have severe apnea. The greater the delay after birth before the first attack of apnea occurred, the better were the chances for survival. Severe apnea seemed to be an extreme form of irregular breathing in premature infants. There was a direct relationship between the degree of irregularity of the respiratory rhythms and the occurrence of long, single periods of apnea. Clinical attacks of severe apnea were observed almost exclusively among infants having the most irregular respiratory rhythms. It is suggested that markedly irregular respiratory rhythms and attacks of severe apnea are the results of enfeebled respiratory centers and that the latter is one of the characteristic features of premature infants with severe respiratory insufficiency (respiratory Group III). Atmospheres of 40% oxygen were associated with longer periods of apnea than was room air. However, better oxygenation of the blood appeared to be maintained through long periods of apnea in 40% oxygen than in room air.