In 73 relative-rate tests involving the sequences of 17 genes between humans and six nonhuman primate taxa, there is only one significant (P less than 0.01) difference in evolutionary rate--i.e., that between human and Old World-monkey psi eta-globin genes. No evolutionary rate difference between humans and Old World monkeys is evident from analysis of 18 other genes with a total length of 6 kb. This and the comparison, between humans and other primate taxa, of new extended psi eta-globin sequences suggest that earlier observations of evolutionary-rate differences between humans and other primates were based on differences that are peculiar to psi eta-globin and that are not representative of the whole genome, which appears to be evolving at a stochastically uniform rate. This is supported by whole-genome single-copy DNA and mitochondrial DNA comparisons, neither of which shows any evidence of evolutionary-rate variation among primate taxa. Uniformity in the evolutionary rate of the DNA of primate and other mammalian taxa is inconsistent with current mammalian fossil-record interpretation. Either there has been a general slowing down in rate across lineages or the fossil record has been misinterpreted.