Evolutionary divergence times can be inferred from molecular distances if a molecular clock can be assumed and if the substitution rate can be estimated. We present new evidence from relative rate tests that the rate of substitution at fourfold degenerate sites of nuclear genome-coding DNA is uniform in primate and rodent lineages. We also review recent relative rate test results showing substitution rate uniformity in the nuclear genome of simian primates. DNA distances between a range of mammalian taxa shows that a molecular clock is inconsistent with many assumed divergence times irrespective of the assumed substitution rate. We find that the substitution rate that implies the best compromise fit with divergence times across the range of taxa is 2.0-2.25 x 10(-9). This range of substitution rates implies a divergence time of humans and chimpanzees of 4.0-3.6 million years ago. This postdates the occurrence of Ardipithecus ramidus and the earliest occurrence of Australopithecus afarensis, suggesting that the common ancestor of humans and chimpanzees was bipedal and that the trait has been lost in chimpanzees rather than gained in humans.