Fluid pressures were estimated from mud weights and wellhead shut-in pressures along a north-south linear trend through the Anadarko basin in southwest Oklahoma. Fluid pressures above hydrostatic start at a depth of about 2.5 km. On a normalized scale where hydrostatic pressure equals 0 and lithostatic pressure equals 1, estimates of fluid pressures were found to range from 0.4 to 0.8 over a depth range of 4-7 km. Using scale analyses and a simple numerical model, we evaluated two end-member hypotheses (compaction disequilibrium and hydrocarbon generation) as possible causes of overpressuring in the Anadarko basin. If compaction disequilibrium is the primary cause of present-day overpressures in the Anadarko basin, the Anadarko basin is required to have an average permeability of 10(-23) m(2) (10(-8) md) or lower. If geopressures in the Anadarko basin result from hydrocarbon generation, average basin permeabilities can e as high as 10(-21) m(2) (10(-6) md). Scaling these average permeabilities down to thicknesses of 100 m or less implies permeabilities lower than 10(-25) m(2) (10(-10) md) are required in the most optimistic scenario. The lowest permeabilities ever measured on sedimentary rocks are in the neighborhood of 10(-22)-10(-23) m(2) (10(-7)-10(-8) md). Thus it is not possible to reconcile the existence of overpressures in the Anadarko basin with classic hydrodynamic theories that maintain that aquicludes do not exist. Either some unknown process is generating excess fluid pressures, or the Anadarko basin contains pressure seals. Geopressure models that invoke compaction disequilibrium and are commonly applied to Cenozoic basins undergoing rapid sedimentation (e.g., the Gulf Coast basin of the southeastern United States) do not appear to apply to the Anadarko basin. The Anadarko basin belongs to a group of cratonic basins that are tectonically quiescent and characterized by the association of abnormal pressures with natural gas.