  A highly precise model for the motion of a rigid Earth is indispensable to
reveal the effects of non-rigidity in the rotation of the Earth from
observations. To meet the accuracy goal of modern theories of Earth rotation of
1 microarcsecond (muas) it is clear, that for such a model also relativistic
effects have to be taken into account. The largest of these effects is the so
called geodetic precession.
  In this paper we will describe this effect and the standard procedure to deal
with it in modeling Earth rotation up to now. With our relativistic model of
Earth rotation Klioner et al. (2001) we are able to give a consistent
post-Newtonian treatment of the rotational motion of a rigid Earth in the
framework of General Relativity. Using this model we show that the currently
applied standard treatment of geodetic precession is not correct. The
inconsistency of the standard treatment leads to errors in all modern theories
of Earth rotation with a magnitude of up to 200 muas for a time span of one
century.

Earth and Planetary Astrophysics;General Relativity and Quantum Cosmology;Geophysics