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Abstract The Antarctic Ice Sheet responds quickly to regime changes, and time lags in its fluctuations are relatively small. During the Pleistocene glacial stages of the Northern Hemisphere, world-wide temperature reductions reduced the plasticity of the ice sheet and made it thicker. The amount of thickening depended on the conditions at the ice base but it was small, for mechanical and thermal reasons. Also, during the northern stages, accumulation over Antarctica was probably less than now, but this too had little effect on the thickness of the ice sheet. The mass budget of the ice sheet alone, without the ice shelves, probably remained strongly positive; the ice sheet probably existed throughout the Pleistocene and is unlikely to disappear in the future. The area of the ice sheet is determined chiefly by the elevation of the “grounding line”, where the peripheral ice cliffs and ice shelves begin to float. During the northern stages, world-wide lowerings of sea-level displaced the grounding line downwards and northwards, and allowed the ice sheet to advance by amounts which account for nearly all the evidence for previous greater glaciations. In summary, the glacial history of most ice-free areas is governed not so much by climatic as by sea-level changes. Therefore, Antarctic glacial fluctuations were dependent on and in phase with those of the Northern Hemisphere. The field evidence from Antarctica has little bearing on the ultimate causes of glacial fluctuations, which might however be determined by field work on the planet Mars.