  The discovery of a flux excess in the far-ultraviolet (UV) spectrum of
elliptical galaxies was a major surprise in 1969. While it is now clear that
this UV excess is caused by an old population of hot helium-burning stars
without large hydrogen-rich envelopes, rather than young stars, their origin
has remained a mystery. Here we show that these stars most likely lost their
envelopes because of binary interactions, similar to the hot subdwarf
population in our own Galaxy. We have developed an evolutionary population
synthesis model for the far-UV excess of elliptical galaxies based on the
binary model developed by Han et al (2002, 2003) for the formation of hot
subdwarfs in our Galaxy. Despite its simplicity, it successfully reproduces
most of the properties of elliptical galaxies with a UV excess: the range of
observed UV excesses, both in $(1550-V)$ and $(2000-V)$, and their evolution
with redshift. We also present colour-colour diagrams for use as diagnostic
tools in the study of elliptical galaxies. The model has major implications for
understanding the evolution of the UV excess and of elliptical galaxies in
general. In particular, it implies that the UV excess is not a sign of age, as
had been postulated previously, and predicts that it should not be strongly
dependent on the metallicity of the population, but exists universally from
dwarf ellipticals to giant ellipticals.
