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We are developing an X-ray computed tomography (CT) system which will be combined with a high resolution animal PET system. This permits acquisition of both molecular and anatomical images in a single machine. In particular the CT will also be utilized for the quantification of the animal PET data by providing accurate data for attenuation correction. A first prototype has been built using a commercially available plane silicon diode detector. A cone-beam reconstruction provides the images using the Feldkamp algorithm. First measurements with this system have been performed on a mouse. It could be shown that the CT setup fulfils all demands for a high quality image of the skeleton of the mouse. It is also suited for soft tissue measurements. To improve contrast and resolution and to acquire the X-ray energy further development of the system, especially the use of semiconductor detectors and iterative reconstruction algorithms are planned.