Thanks to a detailed pulse phase spectroscopy of archival XMM–Newton observations, we discovered narrow and strongly phase-dependent absorption features in the X-ray spectra of two X-ray dim isolated neutron stars (XDINSs), RX J0720.4-3125 and RX J1308.6+2127. The spectral lines show similar properties: they are detected in only 20% of the rotational cycle with an energy of ~ 740 eV and appear to be stable over the timespan covered by the observations. The strong dependence on the pulsar rotation and the narrow width suggest that the features are most likely due to proton cyclotron resonant scattering in a confined magnetic structure close to the stellar surface. The inferred magnetic field in such a loop is of the order of ~ 1014 G, higher than the surface dipolar magnetic field (~ 1 – 3.5 × 1013 G for the XDINSs).