The redox-sensitive trace elements Mo, U and Re can be used as indicators of the oxidation state of the atmosphere in the past. In today's highly oxygenated atmosphere these elements are oxidized during weathering, are transported to the oceans as oxyanions, and are removed from seawater in part by reduction to oxides and/or sulfides in sediments rich in organic matter. Hence such sediments are enriched in these elements. Enrichment is not expected when weathering occurs under an anoxic atmosphere. We have analyzed 37 samples of 2.8 - 1.6 Ga black shales from South Africa and Australia. We have found no correlation between the concentration of Mo, U and Re and that of organic carbon in shales older than 2.3 Ga. On the other hand, there is a strong positive correlation between the concentration of these elements and organic carbon in the 1.6 Ga shale samples from the McArthur and Glyde Basins in Australia. The ratio of Mo, U and Re to organic carbon in these shales is essentially the same as in Phanerozoic black shales. The data indicate that by ca. 1.6 Ga the atmosphere-ocean system had attained an oxidation state similar to today's. The apparent lack of correlation of the concentration of redox-sensitive elements with the organic carbon content of pre-2.3 Ga shales is in agreement with that of other indicators of the evolution of atmospheric oxygen which suggest that the oxygen content of the atmosphere rose dramatically between ca. 2.3 and 2.0 Ga.