Zone plates with improved resolution have been constructed by electron beam lithography. With these zone plates features as small as 30 nm can be imaged without astigmatism. By using the phase shifting property of the zone plate material and by an improved etching technique, groove efficiency values up to 10% have been measured. A new type of foils for the support of the zone plates as well as for the x-ray windows are more stable under synchrotron radiation than the polyimide foils used before and have a higher transmission for x-rays in the `water-window' region. The x-ray microscope installed at BESSY, Berlin, Germany was modified in such a way that the environmental chamber is now placed in air with better access to the specimens under investigation. In addition, a light microscope was incorporated in the x-ray microscope providing a better practicability to adjust object details to the object field of the x-ray microscope, selecting another object or object detail to be investigated, and prefocussing the object for x-ray imaging. With the improved x-ray microscope different wet biological specimens and test structures were investigated, showing features as small as 30 nm. The x-ray microscope using a pulsed plasma x-ray source, installed in Gottingen, Germany was modified in such a way that instead of a zone plate an ellipsoidal mirror is used as the condenser. The pulsed plasma x-ray source was improved too, i.e., the number of pulses needed for an image is reduced.