We present X-ray observations of nine weak-line radio galaxies (WLRGs), optically classified as confirmed or possible LINERs. The data were taken from the Chandra, XMM-Newton, 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 those of 1246-41 (NGC 4696), in which only diffuse emission is detected on the scale of the cluster, and 0334-01 (3C 15), in which only a point source is detected. The nuclear X-ray spectra are well fitted at hard energies by an absorbed power law, with a wide range of photon indices, Γ = 1.5-2.7. Excess absorption over the Galactic value is detected in six of the nine sources, with column densities NH ≈ 1021-1022 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, Lbol/LEdd, and the radiative efficiency η based on the Bondi accretion rates. We find that Lbol/LEdd ~ 10-4-10-6 and η ~ 10-2-10-6 for all the objects in our sample, suggesting radiatively inefficient accretion flows.
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