On the basis of geological arguments, two widely different hypotheses have been proposed for the late-Tertiary glacial history of East Antarctica. Theseinvoke ice-sheet reconstructions ranging from severe glaciation completely burying the Transantarctic Mountains to a situation, in which an unstable EastAntarctic Ice Sheet repeatedly collapses to produce ice-free conditions over interior basins. Experiments were performed with a 3-D model of the Antarctic IceSheet to determine the ice sheet geometries to be expected under various kinds of climatic conditions and the physical mechanisms that may be involved. Theresults supported the concept of a stable East Antarctic Ice Sheet with respect to a climatic warming, and pointed to the glaciological difficulties involved toexplain an ice-free corridor over the Pensacola and Wilkes subglacial basins. The latter event is a crucial element in the 'waxing and waning ice sheethypothesis' and would require a temperature rise of between 17 and 20K above present levels. For a temperature rise of less than 5K, the model actuallypredicts a larger Antarctic Ice Sheet than today as a result of increased snowfall, whereas the West Antarctic Ice Sheet was found not to survive temperatures8-10K above present values. Furthermore, basal temperature conditions in these experiments point to the difficulties involved in raising the ice-sheet base tothe pressure melting point over the large areas necessary to consider the possibility of sliding instability. A further sensitivity study in terms of topographicaland climatic boundary conditions showed that even with a flat bedrock and mass-balance parameters stretched to their limits, the ice sheet would still need atemperature rise of the order of +15K to melt down entirely. Based on these findings, it appears difficult to reconcile a highly variable East Antarctic Ice Sheetwith the modest warmings recorded in, for instance, the deep sea records for the late Neogene.