The adoption of the International Celestial Reference System and the changes of observational strategy call for the use of departure point on the moving equator independently from Earth's orbital motion.  A Nonrotating Origin (NRO), proposed by Guinot, is selected. It depends on the celestial reference pole.  IAU will adopt the Celestial Intermediate Pole (CIP) as the celestial reference pole from 1 January 2003.  The use of NRO in the Celestial Reference System (CRS) is designated as the Celestial Ephemeris Origin (CEO). The use of NRO in the Terrestrial Reference System (TRS) is designated as the Terrestrial Ephemeris Origin (TEO).  In this paper, the concept of the NRO, the coordinate transformation between the CRS and the TRS are reviewed, the coordinates of the celestial reference pole and the positions of the ephemeris origins at a microarcsecond accuracy are provided, the influence on the determination of UT1 of errors in the precession-nutation model, when the ephemeris origins are used, is discussed.  The results show the definition of UT1 based on the ephemeris origins does not require modifications in order to maintain the continuity of UT1 when the models for precession-nutation, pole offset and equinox correction are improved.