Monitoring of the arterial oxygen saturation (SaO2) in two sleeping infants was reported. They were a couple of female twins and had grown up normally after admission to NICU (Neonatal Intensive Care Unit) for a month. We investigated their SaO2 with the puls-oximeter at the terms between the 2nd and the 10th month. There was no significant difference between SaO2 in prone positions (n = 29) and that in supine positions (n = 30). In the infant with the sniffing conditions, however, SaO2 in prone positions seemed to be slightly lower than that in the healthy conditions. The slightly low SaO2 would give no effects on the healthy infants, but it may cause ALTE (Apparent Life Threatening Event) or death from SIDS (Sudden Infant Death Syndrome) to some infants who are not in good health and/or who are prone to get into ALTEA or SIDS. Especially, in the sniffing condition with hyperthermia, as the oxygen dissociation curve sifts to right and SaO2 degradation appears easily, sudden infant death may be possible to happen in prone position.