Perturbations of Earth rotation are currently observed as time variations of universal time UT1-UTC and as changes in the celestial orientation of the axis of the celestial ephemeris pole (CEP) as expressed by five Earth orientation parameters (EOP). On the other hand, dynamical theories of Earth rotation usually describe perturbations of the instantaneous rotation vector. A great improvement in the spatial and the temporal resolution of the EOP determination also raises the problem of the distinction between high-frequency polar motion and nutation. Here we derive the time domain relations between polar motion of the rotation axis and the observed changes of the CEP as well as between the spatial and the terrestrial motion of the CEP. These relations were discussed by Brzeziński (1992a). Here they are presented in a much simpler and direct manner using only matrix transformations between the conventional Terrestrial Reference System and Celestial Reference System in the form proposed by Capitaine et al. (1986) and Capitaine (1990), based upon the concept of the nonrotating origin (Guinot, 1979). These relationships are first obtained in a strict form that enables us to estimate the order of magnitude of errors arising from various approximations. The final linear expressions are used in an algorithm that transforms arbritrary differential equations describing geophysical excitation of polar motion to the form using only the observed quantities as variables. ¿American Geophysical Union 1993