The GALO computer programme was used to model the thermal and burial histories of the Murzuq and Ghadames Basins, Libya. The model was based on recent drilling and seismic data from the basins, and used published deep temperature and vitrinite reflectance measurements. The model provides more accurate results than previous studies which were based on constant geothermal gradients during the basins' histories, and variations in heat flux at the base of the sedimentary cover were chosen so that calculated values of vitrinite reflectance coincide with those observed. The Murzuq Basin and Libyan part of the Ghadames Basin contain similar source rock units but have different burial histories. In the Murzuq Basin, maximum present-day burial depths of Cambrian sediments range from 2200 to 2800 m and only locally reach 3000 - 3600 m; in the Ghadames Basin, however, burial depths can exceed 4-5 km. The burial history of the Murzuq Basin includes several periods of intense erosion and lithospheric heating which produced significant lateral variations in thermal maturity, leading in places to unexpected results. For example, relatively shallow-buried Lower Silurian source rocks in the A-76 area on the flank of the Murzuq Basin have a thermal maturity of R-o = 1.24% which is higher than the maturity of the same interval in more deeply buried areas (wells D1-NC-58 or J1-NC101). In the central part of the Ghadames Basin, the modelling suggests a higher level of thermal maturity for organic matter in Silurian strata (R-o 0.8 to 1.3%), confirming the generation potential of Lower Silurian hot shales. Significant hydrocarbon generation began here in the Late Carboniferous and continues at the present day. Modelling of the Late Devonian (Frasnian) Aouinat Ouinine Formation hot shales suggests limited hydrocarbon generation depending strongly on burial depth, with the main phase of hydrocarbon generation taking place during the final episode of thermal activation in the Cenozoic. In the wells studied in the Ghadames Basin, the oil window extends over a considerable part of the present-day sedimentary column.