  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 O'Dea
\& 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.
