New calculations were performed to investigate the combined response of the Greenland and Antarctic ice sheets to a range of climatic warming scenariosover the next millennium. Use was made of fully dynamic 3-D thermomechanic ice sheet models which were coupled to a two dimensional climate model.The experiments were initialized with simulations over the last two glacial cycles to estimate the present evolution, and subsequently forced with temperaturescenarios resulting from greenhouse emission scenarios which assume equivalent CO2 increases of 2x, 4x, and 8x the pre-industrial value by the year 2130AD, and a stabilization after that. The calculations brought to light that during the next century (short-term effect), the background evolution trend woulddominate the response of the Antarctic ice sheet, but would be negligible for the Greenland ice sheet. On that time scale, the Greenland and Antarctic icesheets would roughly balance one another for the middle scenario (similar to the IPCC96 IS92a scenario), with respective contributions to the world-wide sea-level stand of the order of about ± 10 cm. On the longer term, however, both ice sheets would contribute positively to the worldwide sea-level stand and themost important effect would be from melting on the Greenland ice sheet. Sensitivity experiments highlighted the role of ice dynamics and the height/mass-balance feedback on the results. It was found that ice dynamics cannot be neglected for the Greenland ice sheet, not even on a century time scale, butbecomes only important for Antarctica on the longer term. The latter is related to an increased outflow of ice into the ice shelves and to grounding-line retreatof the West Antarctic ice sheet, which are both found to be sensitive to basal melting below ice shelves and the effective viscosity of the ice shelves.Stretching parameters to their limits yielded a combined maximum rate of sea-level rise of 85 cm/ century, of which 60 cm would originate from theGreenland ice sheet alone.