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Using first-principles density functional calculations, we investigated work functions (WFs) of thin double-walled nanotubes (DWNTs) with outertube diameters ranging from 1 to 1.5 nm. The results indicate that a work function change within this diameter range can be up to 0.5 eV, even for DWNTs with the same outer diameter. This is in contrast with single-walled nanotubes, which show negligible WF changes for diameters larger than 1 nm. We explain the WF change and the related charge redistribution in DWNTs using the charge equilibration model. The protential difficulty in their nanoelectronic device applications.