Traditionally a few limb proportions or total limb lengths have been regarded as indicative of peak running velocity. This is due to physical principles (inferred in- and outvelocities around the joints, stride lengths) and also the observation that fast-moving animals tend to share a number of purported key features which are either absent or not developed to near the same extent in slower moving forms. Previous studies have shown hind limb length and metatarsus/femur ratio to be correlated significantly, albeit modestly with running speed. These studies have nearly all been bivariate analyses. Based on the physical principles, there is reason to suppose that more variables than just m/f ratio could be important as adaptations for fast locomotion, and also that bivariate analyses are too simple. In this study a sample of 76 running mammals was used, with running speeds taken from literature. A number of osteological parameters were discovered to covary significantly with peak running speed, albeit only modestly. Using the information from phylogeny reduced all correlations, often significantly so. Multivariate analyses resulted in markedly higher correlation coefficients. Animals probably do not optimize their anatomy for the purpose of running very fast, which occurs only on rare occasions, but for reducing costs of locomotion. © 2002 The Linnean Society of London, Zoological Journal of the Linnean Society, 2002, 136, 685–714.