The computer tomograph has a tiltable and rotatable gantry (1) which carries a rotary anode x-ray tube (4) and a detector (5) arranged opposite it. The rotation of the gantry and the rotation of the anode take place in opposite directions. The opposite rotation directions result in partial reduction of the gyroscopic forces caused by the tilting of the gantry. The gantry is rotated around an axis (17) perpendicular to the system axis (3) in the direction (18) by a motor. It also rotates in the direction (19) opposite the rotation of the turning anode (14).