Mammalian females are strongly attracted to infants and interact regularly with them. Female baboons make persistent attempts to touch, nuzzle, smell and inspect other females’ infants, but do not hold them for long periods, carry them, or provide other kinds of care for them. Mothers generally tolerate these interactions, but never initiate them. The function of these brief alloparental interactions is not well understood. Infant handling might be a form of reproductive competition if females’ interest in infants causes distress to mothers or harm to their infants. Alternatively, infant handling might be the product of selection for appropriate maternal care if females who are highly responsive to infants are the most successful mothers. We test several predictions derived from these hypotheses with data collected in a free-ranging group of baboons (Papio cynocephalus ursinus) in the Moremi Reserve of Botswana. Infants were most attractive when they were very young. Mothers of young infants were approached by other adult females on average once every 6 min, and other females attempted to handle their infants approximately once every 9 min. By the time infants were a year old, their mothers were being approached only once every 30 min and infants were being handled only once every 5 h. Females were more strongly attracted to other females’ infants when they had young infants of their own, and their interest in other females’ infants declined as their own infants matured. Females seemed to be equally attracted to all infants, but had greater access to offspring of their relatives and subordinate females. Females nearly always grunted as they handled infants. As in other contexts grunts are a reliable predictive signal that non-aggressive behavior will follow, the use of grunts before handling suggests that these interactions were not a form of deliberate harassment.