A diffractometer, having variable center and suitable for performing analysis on hidden or hardly accessible bodies or specimens is described. Said variable center diffractometer is equipped with an analytical unit that comprises: a circle arc structure, called Euler cradle; a radiation beam source and a detector of the said radiation beam; devices for the pointing of the analytical unit; devices for the movements of said analytical unit in the space; devices for rotation of said source and detector along the Euler cradle; characterized by the fact that it comprises also: devices able to rotate said source and detector with respect to an orthogonal axis to the plane containing the Euler cradle; collimators or deflectors firmly placed on the said radiation source and detector.