Abstract: The invention is directed to an X-ray microscope having a pulsed X-ray radiation source which supplies an intensive line radiation such as a plasma focus source. The microscope includes a reflecting condenser which focusses the radiation of the radiation source on the specimen to be investigated and an X-ray optic configured as a zone plate. With the zone plate, the specimen is imaged on an X-ray detector with a high resolution. The above combination of elements makes it possible to free an adequately high amount of X-ray energy at the location of the specimen while providing a high resolution free of image errors so that the required short exposure times are provided for the investigation of living cells.