A sublimation technique has been developed to extract air samples from polar ice cores for subsequent simultaneous measurement of several trace gases by frequency-modulated tunable diode laser absorption spectroscopy. This extraction and analysis technique is shown to be suitable as an extraction method for the determination of concentrations of the greenhouse gases CO2, CH4, and N2O in air samples of ~1--5 cm3 recovered from ice samples of 10--50 g. Air samples from the Siple ice core have been analyzed covering the period between 1772 and 1973. In addition, a few samples from two different ice cores from Vostok station have been analyzed. Our results are in a good agreement with results obtained by other researchers using melting and crushing extraction techniques. This agreement indicates that processes connected with the formation of clathrates in ice under high pressure at greater depths and their destruction after drilling are not affecting the CO2, CH4, and N2O measurements significantly. ¿ 1998 American Geophysical Union