  We report on the results of the cross-correlation of a sample of 903
Ultraluminous IRAS galaxies (ULIRGs) with the ROSAT-All Sky Survey Bright
Source Catalogue and the ROSAT archived pointing observations. The sample of
ULIRGs has been compiled from the PSCz redshift survey. In total, 35 ULIRGs are
securely detected by the ROSAT All-Sky Survey and pointing observations, five
of which are blazars. The statistical properties of these sources in the soft
X-ray band are determined and compared with their properties in other
wavebands. We find that the ratio of the soft X-ray to the far-infrared flux
spans about 5 orders of magnitude and reaches values of about unity. This ratio
is a good indicator of the main energy source of ULIRGs. Those with soft X-ray
to far-infrared flux exceeding 0.01 are probably powered by accretion onto
central supermassive black holes while those with ratios smaller than 0.001 are
probably caused by starbursts or other heating processes, or are Compton thick
sources. Some ULIRGs have energy contributions from both. This ratio is low for
most ULIRGs and hyperluminous infrared galaxies, which explains their low
detection rate by ROSAT and ASCA. We also find that some ULIRGs have a similar
soft X-ray luminosity vs. temperature relation to that for groups of galaxies
and elliptical galaxies, suggesting a common origin of these systems. Our study
also reveals a correlation between the hardness ratio and the soft X-ray
luminosity for Seyfert 1s/QSOs.
