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The suggestion of climatic instability during the last interglacial period (Eem), based on the bottom 10% of the Greenland Ice core Project (GRIP) isotopic profile, has been questioned because the bottom record from the neighboring Greenland Ice Sheet Project 2 (GISP2) core (28 km away) is strikingly different over the same interval and because records of the δ18O of atmospheric O2 from both cores showed unexpected rapid fluctuations. Here we present detailed methane records from the Vostok (Antarctica), GRIP, and GISP2 cores over the relevant intervals. The GRIP and GISP2 data show rapid and large changes in methane concentration, which are correlative with variations of the δ18O of the ice, while the Vostok record shows no such variations. This discrepancy reinforces the suggestion that the bottom sections of the Greenland records are disturbed. By combining the methane data with measurements of δ18O of O2 in the same samples, we attempt to constrain the nature of the stratigraphic disturbance and the age of the analyzed ice samples. Our results suggest that ice layers from part of the last interglacial period exist in the lower section of both ice cores and that some of the apparent climate instabilities in the GRIP core would be the result of a mixture of ice from the last interglacial with ice from the beginning of the last glaciation or from the penultimate glaciation.