The response of the accumulation regions of glaciers to changes in accumulation rate and in surface temperature is calculated by considering pertubations to the ice flow. The analysis is limited to glaciers in whch flow is dominated by internal shear and not by bottom sliding and for which flowliners are geographically paralled. In general, glaciers begin to alter thickness immediately after a change in accumulation rate, but the effect of a change in surface temperature is delayed by the time for this temperature change to penetrate to depth in the glacier. A warming leads to glacial thinning. The amount and timing of the response is very different for different glaciers. Characteristic times are on the order of tens of years for mountain glaciers and ten of thousands of years for the east antarctic ice sheet. As an example, the theory is applied to the ice sheet near Byrd Station, Antarctica. For hypothetical changes in surface accumulation rate and temperature, rates and amounts of thickness change are calculated, and it is found that the measured thinning is probably too fast to have been caused by climatic variation alone. The effects of hypothetical climatic variations on the depth-age and depth-temperature relationships through the ice sheet are also calculated. It is hoped that the theory will prove valuable in the interpreation of future drill hole results.