Many empirical and descriptive models have been proposed since the beginning of the 20th century. In the present study, the powerlaw (Kennelly) and logarithmic (P´eronnet-Thibault) models were compared with asymptotic models such as 2-parameter hyperbolic models (Hill and Scherrer), 3-parameter hyperbolic model (Morton), and exponential model (Hopkins). These empirical models were compared from the performance of 6 elite endurance runners (P. Nurmi, E. Zatopek, J. Väätäinen, L. Viren, S. Aouita, and H. Gebrselassie) who were world-record holders and/or Olympic winners and/or world or European champions.These elite runners were chosen because they participated several times in international competitions over a large range of distances (1500, 3000, 5000, and 10000 m) and three also participated in a marathon.The parameters of these models were compared and correlated.The less accurate models were the asymptotic 2-parameter hyperbolic models but themost accurate model was the asymptotic 3-parameter hyperbolic model proposed by Morton. The predictions of long-distance performances (maximal running speeds for 30 and 60 min andmarathon) by extrapolation of the logarithmic and power-lawmodels were more accurate than the predictions by extrapolation in all the asymptotic models.The overestimations of these long-distance performances by Morton`smodel were less important than the overestimations by the other asymptotic models.
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