The report of the IAU Working Group on Nutation endorsed by Commissions 4, 8, 19 and 31 at the 1979 General Assembly points out that “… the complete theory of the general nutational motion of the Earth about its center of mass may be described by the sum of two components, astronomical nutation, commonly referred to as nutation, which is nutation with respect to a space-fixed coordinate system, and polar motion, which is nutation with respect to a body-fixed system …”. Unlike the situation for the space-fixed frame, there is not an adequate, formally accepted, body-fixed system for this purpose. The Conventional International Origin (CIO) as it is presently defined is no longer acceptable because of recent improvements in observational techniques. The effective lack of this type of terrestrial reference frame limits the complete description of the general nutational motion of the Earth. In the absence of a terrestrial reference frame suitable for specifying the orientation of the Earth, it is suggested that a body-fixed system could be represented formally in a manner analogous to that used to represent the space-fixed frame. This procedure would be quite similar to methods employed currently by the International Polar Motion Service and the Bureau International de l’Heure, and would allow for the use of observations from new techniques in the definition of a terrestrial reference frame to be used to specify the complete nutational motion of the Earth.