  We study the origin of unresolved X-ray emission from the bulge of M31 based
on archival Chandra and XMM-Newton observations. We demonstrate that three
different components are present: (i) Broad-band emission from a large number
of faint sources -- mainly accreting white dwarfs and active binaries,
associated with the old stellar population, similar to the Galactic Ridge X-ray
emission of the Milky Way. The X-ray to K-band luminosity ratios are compatible
with those for the Milky Way and for M32, in the 2 - 10 keV band it is (3.6 +/-
0.2) x 10^27 erg/s/L_sun. (ii) Soft emission from ionized gas with temperature
of about ~ 300 eV and mass of ~ 2 x 10^6 M_sun. The gas distribution is
significantly extended along the minor axis of the galaxy suggesting that it
may be outflowing in the direction perpendicular to the galactic disk. The mass
and energy supply from evolved stars and type Ia supernovae is sufficient to
sustain the outflow. We also detect a shadow cast on the gas emission by spiral
arms and the 10-kpc star-forming ring, confirming significant extent of the gas
in the ``vertical'' direction. (iii) Hard extended emission from spiral arms,
most likely associated with young stellar objects and young stars located in
the star-forming regions. The L_X/SFR ratio equals ~ 9 x 10^38
(erg/s)/(M_sun/yr) which is about ~ 1/3 of the HMXBs contribution, determined
earlier from Chandra observations of other nearby galaxies.
