The oculo-cardiac hypothesis presented here draws attention to the evidence for links between Sudden Unexpected Death in Infants (SUD) - known in America as the Sudden Infant Death Syndrome, also as "cot death" or "crib death" - and the vagally mediated reflex slowing of the heart beat following pressure on the eye. A brief review is made of epidemiologic findings on SUD, including the fact that around 9000 infant fatalities per year are attributed to SUD in the U.S.A. alone. Evidence for excessive vagal discharge as a likely factor in SUD is discussed. The nature of the oculo-cardiac reflex discovered by Aschner is described, with particular attention to those factors which appear to make specific categories of sleeping infant more vulnerable to cardiac arrest in circumstances where this reflex is elicited. The factors include prematurity and an existing electrical instability of the heart. Regarding the manner in which such an oculo-cardiac reflex might in practice be set off, it is suggested that this could occur if the infant slept in such a position that the weight of the head could press the eye against any irregular surface which might exist on the mattress, or any object which was resting on the mattress. Evidence is cited for SUD infants being in fact more likely than controls to sleep in such a position. Children with exophthalmos would be more at risk in this respect. It is stressed that all this evidence is already published, but has not previously been drawn together to show the likelihood of a link between Sudden Dath and the oculo-cardiac reflex.