From ROSAT imaging data we have detections and upper limits for a sample of 26 tailed radio sources in clusters of galaxies mostly from the sample of ODea & Owen (1985). All sixteen of the detected sources are unresolved in the ROSAT PSPC images. The sources bright enough to perform X-ray spectral analysis have power-law indices similar to BL~Lacs and Seyfert galaxies. We find that there is a highly significant correlation between the core radio flux density and the X-ray flux but only a weak correlation between the total radio flux density and the X-ray flux. The trend is similar to that found in earlier studies of 3C radio galaxies with {sl Einstein} and more recently with ROSAT. The result adds an additional constraint on models for the unification of BL~Lac objects with FR~I radio sources. Also this result indicates that the observed enhanced X-ray emission near tailed sources is more likely to be due to nuclear emission rather than substructure in the extended cluster gas.
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