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Previous researchers have adopted linear models to predict athletic running world records, based on records recorded throughout the 20th century. These linear models imply that there is no limit to human performance and that, based on projected estimates, women will eventually run faster than men. The purpose of this article is to assess whether a more biologically sound, flattened “S-shaped” curve could provide a better and more interpretable fit to the data, suggesting that running world records could reach their asymptotic limits some time in the future.Middle- and long-distance running world record speeds recorded during the 20th century were modeled using a flattened S-shaped logistic curve.The logistic curves produce significantly better fits to these world records than linear models (assessed by separating/partitioning the explained variance from the logistic and linear models using ANOVA). The models identify a slow rise in world-record speeds during the early year of the century, followed by a period of “acceleration” in the middle of the century (due to the professionalization of sport and advances in technology and science), and a subsequent reduction in the prevalence of record-breaking performances towards the end of the century. The model predicts that men's world records are nearing their asymptotic limits (within 1–3%). Indeed, the current women's 1500-m world record speed of 6.51 m·s−1 may well have reached its limit (time 3:50.46).Many of the established men's and women's endurance running world records are nearing their limits and, consequently, women's world records are unlikely to ever reach those achieved by men.