Two different kinds of ice flow models, one two-dimensional (2-D) and the other three-dimensional (3-D), have been used to test the importance of the thermodynamic response of the Greenland ice sheet. The basic difference between the two models is that the thermodynamics are neglected in the two-dimensional model, whereas these are incorporated in the three-dimensional model. The 2-D and 3-D models are compared in terms of volume response time and total volume of the ice sheet. Results indicate that the sawtooth character of the ice volume on glacial-interglacial timescales is, among other possible reasons, a result of the thermodynamic coupling. The changes in elevation over the last 130,000 years calculated with the three-dimensional version are 230 m for the Summit drill site and 190 m for the N-GRIP site. The standard deviation of the changes in elevation is 55 m for the Summit site and 43 m for the N-GRIP site. The present-day imbalance is merely a result of the rather constant climate over the last 10 kyr and is not determined by the thermodynamics. Consequently, Pleistocene temperatures do still exist in the ice sheet but are not important for volume calculations of the present-day ice sheet. For short-term perturbation experiments in the future, the pronounced sensitivity of the mass balance will determine the response of the Greenland ice sheet, whereas thermodynamics will play only a minor role. ¿ 1999 American Geophysical Union