An X-ray diffractometer has a mechanism without toothed ring and is suited to move the two legs of a goniometer, on which the source and detector are respectively disposed, at the same time and in a correlated fashion. Each goniometer leg (or linkage) thereby has a common main center of rotation HDP and also one respective auxiliary center of rotation HD1, HD2. The two auxiliary centers of rotation are symmetrically disposed with respect to a symmetry plane E which contains the main center of rotation, and can be moved on a guidance that is symmetrical with respect to the plane E. The main center of rotation can only be moved in the plane E, e.g. along a rail guidance. The movement of the main center of rotation relative to the guidance can be easily driven by means of one single motor.