  The X-ray emission from the faintest X-ray elliptical and S0 galaxies is
characterized by a hard ~5 keV component, and a very soft ~0.2 keV component.
The hard component has generally been regarded as the integrated emission from
low mass X-ray binaries (LMXBs), but the origin of the soft component is
unknown. We present evidence which suggests that LMXBs also exhibit a soft
component, which is responsible for the very soft X-ray emission in the
faintest early-type galaxies. This soft component is present in two Galactic
LMXBs which lie in directions of low Galactic hydrogen column densities, and in
LMXBs in the bulge of M31, which comprise a majority of the X-ray emission in
the bulge of that galaxy. The X-ray spectral characteristics and X-ray-to-blue
luminosity ratios of the bulges of M31 and the Sa galaxy NGC 1291 are very
similar to those of the X-ray faintest early-type galaxies, indicating that
LMXBs are responsible for both soft and hard components in the latter. In
addition, a low temperature interstellar medium might be present in some X-ray
faint galaxies.
