  The beam energy measurement system (BEMS) for the upgraded Beijing
electron-positron collider BEPC-II is described. The system is based on
measuring the energies of Compton back-scattered photons. The relative
systematic uncertainty of the electron and positron beam energy determination
is estimated as 2 \cdot 10^{-5}. The relative uncertainty of the beam's energy
spread is about 6 %.
