An engineered fail-safe system automatically prevents or mitigates the consequences of a system failure. This operational concept can be applied both to the delivery of oxygen to the brain during hypoxia and anaemia, and to the carotid body response to hypoxia and hypercapnia. I aimed to develop simple mathematical models of these fail-safe processes and examine their ability to replicate experimental observations. The intent is to demonstrate the validity of applying the fail-safe concept, not to reveal the details of the physiology involved. The model calculations are based on a single compartment of the relevant tissue in each case that is challenged with a decrease in oxygen supply. The model equation parameters were adjusted to reproduce experimental observations. The fail-safe model of cerebral blood flow control yielded results similar in form to published experimental observations of the cerebral blood flow responses to hypoxia and anaemia. The fail-safe model of carotid body glomus cell control of intracellular hydrogen ion concentration also yielded results similar in form to observations of carotid sinus nerve responses to hypoxia and hypercapnia. The ability of these simple models to simulate experimental observations demonstrates the applicability of the fail-safe concept to oxygen delivery. I suggest that a fail-safe view of oxygen delivery provides novel physiological insight.