The molecular clock hypothesis postulates that the rate of molecular evolution is approximately constant over time. Although this hypothesis has been highly controversial in the past, it is now widely accepted. The assumption of rate constancy has often been taken as a basis for reconstructing the phylogenetic relationships among organisms or genes and for dating evolutionary events. Further, it has been taken as strong support for the neutral mutation hypothesis, which postulates that the majority of molecular changes in evolution are due to neutral or nearly neutral mutations. For these reasons, the validity of the rate constancy assumption is a vital issue in molecular evolution. Recent studies using DNA sequence data have raised serious doubts about the hypothesis. These studies provided support for the suggestion made from immunological distance and protein sequence data that a rate slowdown has occurred in hominoid evolution, and showed, in agreement with DNA hybridization studies, that rates of nucleotide substitution are significantly higher in rodents than in man. Here, rates of nucleotide substitution in rodents are estimated to be 4-10 times higher than those in higher primates and 2-4 times higher than those in artiodactyls. Further, this study provides strong evidence for the hominoid slowdown hypothesis and suggests a further rate-slowdown in hominoid evolution. Our results suggest that the variation in rate among mammals is primarily due to differences in generation time rather than changes in DNA repair mechanisms. We also propose a method for estimating the divergence times between species when the rate constancy assumption is violated.