Two longstanding issues on the molecular clock hypothesis are studied in this article. First, is there a global molecular clock in mammals? Although many authors have observed unequal rates of nucleotide substitution among mammalian lineages, some authors have proposed a global clock for all eutherians, i.e., a single global rate of 2.2 x 10(-9) substitutions per nucleotide site per year. We reexamine this issue using noncoding, nonrepetitive DNA from Old World monkeys (OWMs), chimpanzee, and human. First, using the minimal date of 6 MYA for the human-chimpanzee divergence and more than 2.5 million base pairs of genomic sequences from human and chimpanzee, we estimate a maximal rate of 0.99 x 10(-9) for noncoding, nonrepetitive genomic regions for these two species. This estimate is less than half of the proposed global rate and much smaller than the commonly used rate (3.5 x 10(-9)) for eutherians. Further, using a minimal date of 23 MYA for the human-OWM divergence, we estimate a maximal rate of 1.5 x 10(-9) for both introns and fourfold degenerate sites in humans and OWMs. In addition, with the New World monkey (NWM) lineage as an outgroup, we estimate that the rate of substitution in introns is 30% higher in the OWM lineage than in the human lineage. Clearly, there is no global molecular clock in eutherians. Second, although many studies have indicated considerable variation in the mutation rate among regions of the mammalian genome, a recent study proposed a uniform rate. Using new and existing intron sequence data from higher primates, we find significant rate variation among genomic regions and a positive correlation between the rate of substitution and the GC content, refuting the claim of a uniform rate.