We present an analysis of X-ray data, taken with ROSAT, for a well-defined
sample of low-power radio galaxies from the Bologna B2 catalogue. Where pos
sible, the HRI has been used in order to take advantage of the high spatial
resolution provided by this instrument. A variety of models are fitted to
radial profiles in order to separate the resolved and unresolved X-ray emis
sion from the galaxies. We demonstrate a strong, approximately linear, corr
elation between the luminosities of the unresolved X-ray components and the
5-GHz luminosities of the radio cores in this sample. This suggests a phys
ical relationship between the soft X-ray emission of radio galaxies and the
jet-generated radio core emission. We infer a nuclear jet-related origin f
or at least some of the X-ray emission.