Volume changes of the Greenland and Antarctic ice sheets constitute the largest source of uncertainty to explain the current rate of sea-level rise and have the potential to signicantly increase this rate in future warmer climates. Crucial aspects are how climatic changes will affect the ice sheet's mass balance and how ice dynamics will react to the imposed environmental forcing. These questions were addressed with 3-D thermomechanical ice sheet/ice shelf models submitted to a range of climatic scenarios derived from the ECHAM4/OPYC3 high-resolution GCM results and from energy-balance climate models. The experiments were initialized with simulations over the last two glacial cycles to estimate the longer-term background evolution. It is found that the polar ice sheets may contribute more negatively to sea-level in the 21st century than previously thought, but would become dominant for sea-level rise after a few centuries, with the most important effect coming from the Greenland ice sheet. Ice dynamics tends to produce a counteracting effect on the short term, but can signifcantly speed up the response after that. The model does not produce a collapse of the marine West Antarctic Ice Sheet, not even for large warming and melting rates below the ice shelves of 10 m/year.