A nonsteady ice-flow model that explicitly includes longitudinal stresses is used to study the effects of marginal changes on the interior portions of an ice sheet. Sea-level rise is found to cause a wave of thinning to propagate upglacier, and this wave is slowed, diffused, and damped. At the ice divide at dome C in central East Antarctica, post-Wisconsinan sea-level rise is modeled as having caused 110 m thinning, with response now 70% complete. If accumulation rates increased by 10% at the same time, then calculated net thinning has been only 75 m. Ice-sheet response to changes in sea level and accumulation rate is relatively rapid; response to temperature changes is an order of magnitude slower. Response times are shorter if the marginal position of an ice sheet is controlled.