For the investigation of specimens in their natural wet state the wavelength range of the water window is well suited. The transmission of water is the best at lambda = 2.4 run, i.e. objects in a water layer of up to 10 mum thickness can be investigated. Studies with an X-ray microscope at the electron storage ring BESSY in Berlin were performed. An X-ray microscope with a pulsed plasma source is under development.