The results of numerical calculations of intensity and spectra of optical emissions from red sprites produced by runaway air breakdown in the atmosphere are presented. It is shown that the optical emissions from red sprites consist of two components: (1) short-term (t≈0.3--2 ms) emissions produced as a result of dissipation of an energetic electron beam in air; (2) long-term (t≈2--10 ms) emissions produced by a population of low-energy electrons in an electric field. The long-term optical emissions are calculated for all low-energy electrons, including the secondary low-energy electrons produced by the relativistic electron beam, ambient background electrons, and electrons produced as a result of regular breakdown. The theoretical results are compared with observational data. ¿ 1998 American Geophysical Union