In 1923, Hill and Lupton pointed out that for Hill himself, 'the rate of oxygen intake due to exercise increases as speed increases, reaching a maximum for the speeds beyond about 256 m/min. At this particular speed, for which no further increases in O2 intake can occur, the heart, lungs, circulation, and the diffusion of oxygen to the active muscle-fibres have attained their maximum activity. At higher speeds the requirement of the body for oxygen is far higher but cannot be satisfied, and the oxygen debt continuously increases'. In 1975, this minimal velocity which elicits maximal oxygen uptake (VO2max) was called 'critical speed' and was used to measure the maximal aerobic capacity (max Eox), i.e. the total oxygen consumed at VO2max. This should not be confused with the term 'critical power' which is closes to the power output at the 'lactate threshold'. In 1984, the term 'velocity at VO2max' and the abbreviation 'vVO2max' was introduced. It was reported that vVO2max is a useful variable that combines VO2max and economy into a single factor which can identify aerobic differences between various runners or categories of runners. vVO2max explained individual differences in performance that VO2max or running economy alone did not. Following that, the concept of a maximal aerobic running velocity (Vamax in m/sec) was formulated. This was a running velocity at which VO2max occurred and was calculated as the ratio between VO2max (ml/kg/min) minus oxygen consumption at rest, and the energy cost of running (ml/kg/sec). There are many ways to determine the velocity associated with VO2max making it difficult to compare maintenance times. In fact, the time to exhaustion (tlim) at vVO2max is reproducible in an individual, however, there is a great variability among individuals with a low coefficient of variation for vVO2max. For an average value of about 6 minutes, the coefficient of variation is about 25%. It seems that the lactate threshold which is correlated with the tlim at vVO2max can explain this difference among individuals, the role of the anaerobic contribution being significant. An inverse relationship has been found between tlim at vVO2max and VO2max, and a positive one between vVO2max and the velocity at the lactate threshold expressed as a fraction of vVO2max. These results are similar for different sports (e.g. running, cycling, kayaking, swimming). It seems that the real time spent at VO2max is significantly different from an exhaustive run at a velocity close to vVO2max (105% vVO2max). However, the minimal velocity which elicits VO2max, and the tlim at this velocity appear to convey valuable information when analysing a runner's performance over 1500m to a marathon.