We describe results from an ongoing experiment in Greenland, in which we are using absolute gravity and continuous Global Positioning System (GPS) measurements to study vertical crustal motion at two locations along the edge of the ice sheet: Kellyville, located about one third of the way up the western ice margin, and Kulusuk, located along the eastern ice margin at about the same latitude as Kellyville. The GPS measurements suggest average crustal uplift rates of -5.8¿1.0 mm/yr at Kellyville and -2.1¿1.5 mm/yr at Kulusuk. There have not yet been enough absolute gravity occupations to permit useful secular gravity solutions at either location. The negative uplift rate at Kellyville is consistent with independent archeological and historical evidence that the southwestern edge of the continent has been subsiding over the last 3000 years, but it is inconsistent with estimates of the Earth's continuing viscoelastic response to melting ice during the early Holocene, which predict that Kellyville is likely to be uplifting, rather than subsiding, by 2.0¿3.5 mm/yr. The resulting -7.8¿3.6 mm/yr discrepancy between the observed and predicted uplift rates is too large to be caused by loading from present-day changes in nearby ice. However, it is consistent with independent suggestions that the western ice sheet margin in this region may have advanced by ≈50 km during the past 3000--4000 years. If this advance did occur and if the crustal subsidence it induces is not removed from altimeter measurements of Greenland ice sheet elevations, then the altimeter solutions could underestimate the true snow/ice thickness change by 5--10 mm/yr along portions of the western margin of the ice sheet. ¿ 2001 American Geophysical Union