  We present X-ray observations of nine Weak-Line Radio Galaxies (WLRGs),
optically classified as confirmed or possible Low Ionization Nuclear
Emission-line Regions (LINERs). The data were taken from the Chandra, XMM, and
BeppoSax archives. The Chandra images typically show complex X-ray
morphologies, with hard (2-10 keV) point sources embedded in diffuse soft
(0.3-2.0 keV) emission in all cases except 1246-41 (NGC 4696), where only
diffuse emission is detected on the scale of the cluster, and 0334-01 (3C 15),
where only a point source is detected. The nuclear X-ray spectra are well
fitted at hard energies by an absorbed powerlaw, with a wide range of photon
indices, Gamma=1.5-2.7. Excess absorption over the Galactic value is detected
in 6/9 sources, with column densities NH approximately 10^21-22 cm^-2. A
thermal component is required at softer energies, in agreement with the results
of the spatial analysis. We find that there is no correlation between the core
X-ray luminosity and the radio core dominance parameter, suggesting that the
bulk of the core X-ray emission is not beamed, but rather is isotropic and thus
likely related to the accretion flow. In an attempt to constrain the nature of
the accretion flow, we calculate the ratios of bolometric to Eddington
luminosities L_bol/L_Edd, and the radiative efficiency eta based on the Bondi
accretion rates. We find that L_bol/L_Edd ~10^-4 - 10^-6 and eta ~10^-2 - 10^-6
for all the objects in our sample, suggesting radiatively inefficient accretion
flows.
