MP2 and CCSD(T) calculations are used to analyse the structures and vibrational spectra of HRgF molecules, where the rare gas atom is He, Ne, Ar, Rr, Xe or Rn. We extend the analysis of the vibrational spectra of these molecules to include anharmonic corrections for the most likely candidates for experimental detection, i.e., HArF, HKrF, HXeF, and their deuterated isotopomers. The anharmonic correlation-corrected vibrational self-consistent-field (CC-VSCF) calculations are used for this, and fundamental, overtone and combination frequencies and their absorption intensities are computed.