The soft X-ray emission from both galaxies NGC 1808 and NGC 1792, which we investigated using the ROSAT HRI and PSPC, comes most probably from X-ray binaries and/or from hot ionized gas in powerful supernovae and supernova remnants. The distribution of the soft X-ray emission in NGC 1808, which is very well correlated with the distribution of "radio knots" in the central starburst, suggests that hot gas dominates the emission in the ROSAT band. This is consistent with the results of PSPC observations by Junkes et al. (1994). The total soft X-ray luminosity in the ROSAT band of NGC 1808 of 1.2 x 10^41^ ergs s^-1^ is relatively high compared with other nearby starburst galaxies. Soft X-ray emission of diffuse hot ionized gas that is associated with the outflow traced by the conspicuous dust filaments protruding from the plane has 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-ray radiation from NGC 1792 is more likely to be dominated by a population of high-mass X-ray binaries or young powerful supernovae which are associated with the high-level star formation going on in the very prominent 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 accreting neutron star. The peaks of some of these soft X-ray luminous sources are offset with respect to the H II regions by a few hundred parsecs. Accordingly, if the soft X-ray sources should originate from the H II regions, their relative velocities with respect to the ambient medium have to be as high as ~100 km s^-1^.
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