At present the age of ice from ice cores taken at depths where the seasonal isotope fluctuations no longer are measurable is estimated from the Dansgaard-Johnsen-Nye analysis of the longitudinal thinning of ice sheets. A significant error occurs in such an age estimate if ice cores are taken from a hole drilled through ice that has flowed from a region of the ice sheet where ice slides over its bed to a region where it cannot slide over its bed. The Camp Century drill hole is in ice which may have had such a flow history. In the zone where sliding ceases to take place, the horizontal ice velocity decreases in magnitude in the lower part of the ice sheet while it increases in the upper part. The average ice velocity remains unchanged in value. As a consequence the upper part of the ice sheet is stretched and the lower part is compressed as ice moves through the sliding-no sliding transition zone. The upper part is stretched to a strain of the order of 1/2 and the lower part is compressed to a strain that is of the order of 1/2. The age of ice from the Dansgaard-Johnsen-Nye analysis is underestimated; the error in the age is of the order of h/a, where h is the ice thickness and a is the accumulation rate. (Larger errors occur if the theory of Johnsen et al. is used to determine the age of the ice.) An error in age of a similar magnitude exists if ice flows from a region in which sliding does not take place into a region in which it does. The Byrd Station drill hole is in ice which probably has such a flow history. In this situation the age of the ice is overestimated. If the annual isotope fluctuations are detectable the sliding-no sliding zone effect will make it appear that a sudden change in the accumulation rate occurred at the time the ice at the upper surface of the ice sheet passed over this zone.