Osmosis and pervaporation of water through the roof of all-polyimide channels of 500 nm height is described. The phenomena cause both a liquid flow in the channels and a concentration change of dissolved salt. Both effects are amplified due to the thin channel roof and the small channel height. Osmotic movement of demineralized water was observed towards a salt solution and towards ethanol and isopropanol. Water movement by pervaporation was observed from a salt solution towards the atmosphere. Flow velocities of up to 70 �?��m/s were generated in the channels. The results are in accordance with predictions from the solution-diffusion model for membrane transport. The observed phenomena can be applied in a nanofluidic osmotic pump or for an osmotic or pervaporative concentrator.