An enduring hypothesis in exercise physiology holds that a limiting cardiorespiratory function determines maximal exercise performance as a result of specific metabolic changes in the exercising skeletal muscle, so-called peripheral fatigue. The origins of this classical hypothesis can be traced to work undertaken by Nobel Laureate A. V. Hill and his colleagues in London between 1923 and 1925. According to their classical model, peripheral fatigue occurs only after the onset of heart fatigue or failure. Thus, correctly interpreted, the Hill hypothesis predicts that it is the heart, not the skeletal muscle, that is at risk of anaerobiosis or ischaemia during maximal exercise. To prevent myocardial damage during maximal exercise, Hill proposed the existence of a 'governor' in either the heart or brain to limit heart work when myocardial ischaemia developed. Cardiorespiratory function during maximal exercise at different altitudes or at different oxygen fractions of inspired air provides a definitive test for the presence of a governor and its function. If skeletal muscle anaerobiosis is the protected variable then, under conditions in which arterial oxygen content is reduced, maximal exercise should terminate with peak cardiovascular function to ensure maximum delivery of oxygen to the active muscle. In contrast, if the function of the heart or some other oxygen-sensitive organ is to be protected, then peak cardiovascular function will be higher during hyperoxia and reduced during hypoxia compared with normoxia. This paper reviews the evidence that peak cardiovascular function is reduced during maximal exercise in both acute and chronic hypoxia with no evidence for any primary alterations in myocardial function. Since peak skeletal muscle electromyographic activity is also reduced during hypoxia, these data support a model in which a central, neural governor constrains the cardiac output by regulating the mass of skeletal muscle that can be activated during maximal exercise in both acute and chronic hypoxia.