A small torsional couple is applied about the axis of symmetry of a system of two elastic spheres (or solids of revolution) which have been pressed together by a force perpendicular to their common tangent plane. This problem may be reduced to a “problem of the plane,” and it has been found that in the absence of slip on the interface, the tangential traction is singular on the bounding circle. Hence the assumption of no slip is physically untenable. In the present solution allowance is made for slip by assuming that the tangential component of traction, for the area over which slip has progressed, is equal to the product of a constant friction coefficient and the normal or Hertzian distribution. A continuous expression for the traction is developed. A formula relating the radial depth of penetration of slip to the magnitude of the applied moment is given, and another relating this moment to the rotation of the contact surface of one of the bodies with respect to remote points in that body.