The most popular types of LiF-based thermoluminescent (TL) detectors, LiF:Mg,Ti (MTS-N) and LiF:Mg,Cu,P (MCP-N), have been investigated, with respect to their dose (fluence) response and relative TL efficiency to different ion species. The detectors were irradiated using the nitrogen, iron, krypton and xenon ion beams, at energies ranging from 5.0 to 9.3 MeV/n. Supra- and sublinear response was found, for the MTS-N and MCP-N, respectively, similarly as observed for γ-rays. However, the level of nonlinearity of response of studied detectors is strongly reduced by increasing values of the ion ionization density (no supralinearity for Xe ions, for MTS-N, within calculated uncertainties). The growth of high-temperature TL peaks, with increasing ionization density, was observed for MCP-N, what was not previously reported. At the whole range of applied energies higher efficiencies were noted for MTS-N, for all ion species. A decrease of the efficiency with decrease of the ion energy was confirmed, for both types of studied detectors. At a given energy, higher efficiency was observed for lighter ions, because of the lower ionization density. Significantly higher decrease of the efficiency was measured for MCP-N. The obtained results remain in a general agreement with other theoretical and experimental data. The data collected for the highest doses (fluences) of Xe ions will be used for testing a recently proposed method of experimental verification of radial dose distribution models.