The soft X-ray emission from both galaxies NGC 1808 and NGC 1792, whic
h we investigated using the ROSAT HRI and PSPC, comes most probably fr
om X-ray binaries and/or from hot ionized gas in powerful supernovae a
nd supernova remnants. The distribution of the soft X-ray emission in
NGC 1808, which is very well correlated with the distribution of ''rad
io knots'' in the central starburst, suggests that hot gas dominates t
he emission in the ROSAT band. This is consistent with the results of
PSPC observations by Junkes et al. (1994). The total soft X-ray lumino
sity in the ROSAT band of NGC 1808 of 1.2 x 10(41) ergs s(-1) is relat
ively high compared with other nearby starburst galaxies. Soft X-ray e
mission of diffuse hot ionized gas that is associated with the outflow
traced by the conspicuous dust filaments protruding from the plane ha
s been detected. Its luminosity in the ROSAT band is >3 x 10(39) ergs
s(-1), i.e., several percent of the total soft X-ray luminosity. Thus,
NGC 1808 is another example for a ''superwind'' galaxy. The soft X-ra
y radiation from NGC 1792 is more likely to be dominated by a populati
on of high-mass X-ray binaries or young powerful supernovae which are
associated with the high-level star formation going on in the very pro
minent H II regions along its spiral arms, with possibly an additional
contribution of diffuse hot ionized gas. The soft X-ray luminosities
of individual sources lie in the range of 5 x 10(38) to, 2.7 x 10(39)
ergs s(-1), thus exceeding by far the Eddington luminosity of an accre
ting neutron star. The peaks of some of these soft X-ray luminous sour
ces are offset with respect to the H II regions by a few hundred parse
cs. Accordingly, if the soft X-ray sources should originate from the H
II regions, their relative velocities with respect to the ambient med
ium have to be as high as similar to 100 km s(-1).