An X-ray diagnostic apparatus has a luminescent storage screen for the latent storage of an X-ray image, an X-ray exposure apparatus for producing an X-ray beam, a readout apparatus system with which the storage luminescent screen is excited to luminescence by scanning with a source of radiation, a detector for the acquisition of the light emitted by the storage luminescent screen, and an image playback system. For the scanning, the storage luminescent screen is guided through an opening of a rectangular supporting structure and is held in the scanning region by air bearings attached to the supporting structure on both sides of the opening. A line-shaped source of stimulation radiation and a line-shaped light detector are mounted to the supporting structure.