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Dedicated line observations of CH4 rotational lines performed with Herschel/PACS and HIFI in 2009-2011 provide new inferences of the mean methane profile in the upper tropospheres and stratospheres of Uranus and Neptune. At Uranus, CH4 is found to be near saturation, with a ~9×10-4 tropopause/lower stratosphere mole fraction. This is nominally six times larger than inferred from Spitzer in 2007, although reconciliation may be possible if the CH4 abundance decreases sharply from ~100 to 2 mbar. This unexpected situation might reflect heterogeneous conditions in Uranus' stratosphere, with local CH4 depletions and heating associated with downwelling motions. Higher CH4 abundances compared to values inferred under solstitial conditions by Voyager in 1989 suggest that atmospheric mixing is effectively subdued at high latitudes and/or is time-variable. At Neptune, the mid-stratosphere CH4 abundance is (1:15 ± 0:10) × 10-3, in agreement with earlier determinations and indicative of either leakage through a warmer polar region or upwelling at low or middle latitudes. On both planets, spatially resolved observations of temperature and methane in the stratosphere are needed to further identify the physical processes at work. [ABSTRACT FROM AUTHOR]