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We have analyzed ROSAT observations of several nearby face-on spiral galaxies and find significant unresolved X-ray emission in 0.1-2 keV energy band. In all galaxies, the emission is strong at the center and becomes fainter toward the outer edge. In the 0.1-0.4 keV energy band, there is an apparent deficiency in X-ray surface brightness around the outer edges of the galaxies. This can be interpreted as absorption of extragalactic X-ray emission by interstellar matter in the galaxies, thus providing an interesting lower limit on the cosmic X-ray background at these energies.