This paper describes measurements of concentrations of cosmogenic 26Al, 10Be and 21Ne in quartz from bedrock surfaces in the Transantarctic Mountains where stratigraphic and geomorphic evidence shows that the surfaces were covered by ice in the past, but were not glacially eroded during periods of ice cover. It then explores to what extent this information can be used to learn about past ice sheet change. First, cosmogenic nuclide concentrations in sandstone bedrock surfaces at two sites in the McMurdo Dry Valleys near 77°S are consistent with an equilibrium between nuclide production and loss by surface erosion and radioactive decay. They are most easily explained by a scenario in which: i) sites more than c. 100 m above the present ice surface were almost never ice-covered and eroded steadily at 0.5–1.5 m Ma-1, and ii) sites near the present ice margin experienced similar erosion rates when ice-free, but have been covered by cold-based, non-erosive glacier ice as much as half of the time during the past several million years. Nuclide concentrations in granite bedrock at a site in the Quartz Hills near 85°S, on the other hand, have not reached production-erosion equilibrium, thus retaining evidence of the time they were first exposed to the cosmic ray flux. Nuclide concentrations at these sites are most easily explained by 4–6 Ma exposure, extremely low erosion rates of 5–10 cm Ma-1 during periods of exposure, and only very short periods of cold-based, non-erosive ice cover.