A low-temperature study of the thermoluminescent dosimeter material, lithium tetraborate (Li 2 B 4 O 7 ) doped by Cu, has been carried out by the methods of electron paramagnetic resonance (EPR) and time-resolved polarization spectroscopy using 4-20 eV synchrotron radiation and 1 μs Xe flash lamp pulses in the region 3-6 eV. The observed EPR spectra of an unpaired hole with strong d-character and characteristic hyperfine splittings can be ascribed to Cu 2+ substituted at a Li lattice site and displaced due to relaxation. The results on the Cu + -related luminescence strongly support the conclusion about a low-symmetry position of copper impurity ions in the lithium tetraborate lattice. The temperature dependence of the decay kinetics of the Cu + -related 3.35 eV emission indicates a triplet nature for the relaxed excited state of the Cu + centres. An off-centre position of the Cu + ion in the relaxed excited state is suggested.