The present state of balance of the Greenland ice sheet is an important initial condition to assess the ice sheet's contribution to future sea levels. From aphysical point of view, regarding the long time scales introduced by isostasy, thermo-mechanical coupling and the slow advection of harder Holocene ice inthe basal shear layers, it is unlikely that the Greenland ice sheet would have adjusted completely to its past history. Based on various methods and only alimited amount of measurements, it seems that at present an imbalance of up to 30% of the annual mass turnover cannot be detected in a definite way (Warrickand Oerlemans, 1990). Here I use an alternative method to approach this problem, and obtain the imbalance by first simulating the past history of the ice sheetand subsequently analyzing the evolution pattern which results for the present day. Theoretically, this approach would be exact provided both the pastboundary conditions (mass balance, surface temperature, ...) over a time scale at least as long as the longest response time scale of the system and the icedynamics were perfectly described.I use a 3-D, time-dependent thermomechanical ice sheet model which includes all of the relevant mechanisms believed to play a role in the ice sheet'sevolution. The environmental forcing is made up by both prescribing the eustatic sea level stand, which determines the coast line beyond which the ice sheetcannot expand, and a uniformly distributed background temperature change, which drives the mass-balance model. The latter consists of two components: theaccumulation part is based on presently observed values and varies by 5.3% for every degree of temperature change. The ablation model is based on thedegree-day method and accounts for the daily and annual temperature cycle, a different degree-day factor for ice and snow melting and superimposed iceformation.A steady-state simulation of the ice sheet in a glacial climate was used as an initial configuration at 135000 years ago, when calculations started. The modelforcing consists of a temperature record for central Greenland, which was assembled from various sources. This record resolves features down to a period of100 years, meaning that only the somewhat longer-term trend is expected to show up in the results.The calculations indicate that the ice sheet as a whole is at present thickening slightly at a mean rate of 14 km3 of ice or almost 1 cm/year, corresponding to aworld-wide sea-level lowering of 3.5 mm during the last hundred years. However, large spatial differences occur. Central and northern parts high up in theaccumulation area show a slight thinning which is mainly due to a slow but consistent basal warming in response to the last glacial- interglacial transition.Marginal thinning, most notably in the northeast and along major parts of the west coast, on the other hand, is principally due to increased melting caused byhigher temperatures subsequent to the Little Ice Age. The most striking feature is a rather important thickening in the southwestern part of the ice sheet, whichappeared to be robust against all realistic changes in environmental and ice-dynamical factors. It is suggested that this represents a long-term trend caused by apurely dynamic reaction to the geometry which came out of the last glacial-interglacial transition.