These cars and earlier 5 and 7 series cars, use a tension or thrust arm in the front suspension geometry, which has a large rubber busing on the end that mounts to the chassis. When this bushing wears, the suspension is able to move forward and aft more than is normal and any slight out of round or out of balance wheel will magnify the movement into the classic 50-65mph shimmy. Have the bushings checked, replaced if needs be and a good balancing of your wheels and all will be good...
Garey