  Diffuse X-ray emission from the Magellanic Clouds (MCs) is studied by using
all the archival data of pointed ROSAT Position Sensitive Proportional Counter
(PSPC) observations. For this purpose, contributions from the point and
point-like sources in the ROSAT High Resolution Imager (HRI) and PSPC source
catalogues are eliminated and periods of high solar activity are excluded. The
spectral analysis yielded characteristic temperatures of 10^6 - 10^7 K for the
hot thin plasma of the ISM which extends over the whole Large Magellanic Cloud
(LMC) and the Small Magellanic Cloud (SMC). The total unabsorbed luminosity in
the 0.1 - 2.4 keV band within the observed area amounts to 3.2 x 10^38 erg s^-1
in the LMC and 1.1 x 10^37 erg s^-1 in the SMC, each with an uncertainty of
-40%, +100%. The X-ray luminosity of the LMC is comparable to that of other
nearby galaxies with pronounced star formation. In the LMC, hot regions were
found especially around the supergiant shell (SGS) LMC 4 and in the field
covering SGS LMC 2 and LMC 3. Highest temperatures for the SMC were derived in
the southwestern part of the galaxy. The diffuse X-ray emission is most likely
a superposition of the emission from the hot gas in the interior of shells and
supershells as well as from the halo of these galaxies.
