Ice core work on Greenland has produced dramatic evidence for an instability of the climate system in the North Atlantic sector. In this paper, we provide climate modeling results indicating another possible example of a multiple equilibrium climate state, where such behavior might apply to the ice sheet itself. Baseline sensitivity experiments, in which the Greenland Ice Sheet was removed, simulate summer temperatures on Greenland of about 10 ¿C. This number varied between about 6 and 14 ¿C depending on specification of vegetation type, elevation of Greenland, and orbital forcing. The implied hysteresis indicates that the present geographic configuration may have been sufficient to maintain an ice-free state prior to formation of the ice cap. Explanations for formation of the ice sheet therefore present a dilemma. Four possibilities involve undocumented Miocene-Pliocene CO2 excursions to values lower than present, a high sensitivity of the climate system, a variable sensitivity of the climate system, or significant problems with the climate model. A variable sensitivity is consistent with our results indicating a multiple steady state climate for Greenland. Although most CO2 scenarios do not predict a collapse of the Greenland Ice Sheet in the future, our results suggest that if it did, present boundary conditions may be sufficient to maintain Greenland in an ice-free environment even after the greenhouse effect has dissipated. ¿ American Geophysical Union 1995