This paper summarizes the results of Rock-Eval pyrolysis data of 43 shale samples collected from the latest Ordovician - earliest Silurian (Tanezzuft Formation) interval in the CASP JA-2 well at Jebel Asba on the eastern margin of the Kufra Basin, SE Libya. The results are supported by analysis of cuttings samples from an earlier well of uncertain origin nearby, referred to here as the UN-REMSA well. The Tanezzuft Formation succession encountered in the JA-2 well can be divided into three intervals based on Rock-Eval pyrolysis data. Shales in the shallowest interval (20 - 46.5 m depth) are altered probably by weathering and lack significant amounts of organic matter. Total organic carbon (TOC) contents of shales from the intermediate interval (46.5 - 68.5 m depth) vary between 0.19 and 0.75 wt%. Most samples in this interval have very limited source rock potential although a few have Hydrogen Index (HI) values up to 378 mg S-2/g TOC.T-max values of 422 - 426 degrees C indicate the organic matter is immature. Shales from the deepest interval (68.5 - 73.9 m depth) are diagenetically altered, perhaps by fluids flowing along a nearby fault or along the contact between the Tanezzuft Formation and the underlying Mamuniyat Formation and apparently lack any organic matter. Cuttings samples from the UN-REMSA well have TOC contents of 0.48-0.87 wt%, HI values of 242-252 mg S-2/g TOC, and T-max values of 421-425 degrees C. These results offer little support for the presence of the basal Silurian (Tanezzuft Formation) source rock which is prolific elsewhere in SW Libya and eastern Algeria and, together with the overall immaturity of the equivalent section, reduces the probability of finding major oil reserves in the eastern part of the Kufra Basin.