We measured the abundance of cosmo- genic 10 Be and 26 Al in 22 samples collected from five striated granite, metarhyolite, and quartzite outcrops in south-central Wiscon- sin that were covered by the late Wisconsin Laurentide Ice Sheet. In two outcrops, mea- sured nuclide abundances are consistent with the existing radiocarbon chronology of ice retreat. In three outcrops, nuclide abun- dances were up to eight times higher than predicted by the radiocarbon chronology. At these three sites, several thousand years of ice flow eroded only centimeters to deci- meters of rock, allowing a significant quan- tity of nuclides (10 5 two samples carry the equivalent of .150,000 yr of surface exposure, even though they were covered by ice during the last-glacial-maximum advance. Samples highest on the landscape or in plucked ar- eas have less inheritance than those from the lee sides of large hills or lower in the landscape. Three quartzite samples collect- ed ;10 km up-ice from the margin contain three to four times the expected nuclide abundance (10 5 to 10 6 atoms per gram of quartz). In contrast, eight other quartzite and granite samples from two outcrops .50 km up-ice from the former margin contain only 10 5 atoms of 10 Be per gram of quartz, consistent with late Pleistocene ex- posure and little, if any, nuclide inheri- tance. This relationship between glacial erosion and distance from the former ter- minus is consistent with a marginal zone of minimal subglacial erosion; the ice was ei- ther frozen to its bed there, or the ice thick- ness and duration of ice cover were less near the terminus. These data, together with simple model- ing of nuclide production by deeply pene- trating muons, suggest that many meters of rock must be removed to reduce inheri- tance to negligible levels (,1000 yr) in con- tinental terrains with low long-term erosion rates. Our results indicate that cosmogenic dating of exposed bedrock surfaces near former ice margins or in areas where ice was frozen to the bed may be uncertain, and in some cases impossible, because nu- clides are inherited from prior periods of cosmic-ray exposure. Unfortunately, striat- ed glacial outcrops that can be used to dem- onstrate most easily the assumption of ''no postglacial erosion'' are also the most likely to have undergone little glacial erosion. This finding suggests that cosmogenic- nuclide production rates based on glacially striated surfaces may include cosmogenic nuclides inherited from prior exposure.