The hypothesis of the molecular evolutionary clock asserts that informational macromolecules (i.e., proteins and nucleic acids) evolve at rates that are constant through time and for different lineages. The clock hypothesis has been extremely powerful for determining evolutionary events of the remote powerful for determining evolutionary events of the remote past for which the fossil and other evidence is lacking or insufficient. I review the evolution of two genes, Gpdh and Sod. In fruit flies, the encoded glycerol-3-phosphate dehydrogenase (GPDH) protein evolves at a rate of 1.1 x 10(-10) amino acid replacements per site per year when Drosophila species are compared that diverged within the last 55 million years (My), but a much faster rate of approximate to 4.5 x 10(-10) replacements per site per year when comparisons are made between mammals (approximate to 70 My) or Dipteran families (approximate to 650 My), or multicellular kingdoms (approximate to 1100 My). The rate of superoxide dismutase (SOD) evolution is very fast between Drosophila species (16.2 x 10(-10) replacements per site per year) and remains the same between mammals (17.2) or Dipteran families (15.9), but it becomes much slower between animals phyla (5.3) and still slower between the three kingdoms (3.3). If we assume a molecular clock and use the Drosophila rate for estimating the divergence of remote organisms, Drosophila rate for estimating of 2,500 My for the divergence between the animal phyla (occurred approximate to 650 My) and 3,990 My for the divergence of the kingdoms (occurred approximate to 1,100 My). At the other extreme, SOD yields divergence times of 211 My and 224 My for the animal phyla and the kingdoms, respectively. It remains unsettled how often proteins evolve in such erratic fashion as GPDH and SOD.