The thermoluminescence efficiency, ?, of LiF:Mg,Cu,P (MCP-N detectors, commercially produced at the INP, Krakow, Poland), relative to 662 keV 137Cs gamma rays, has been measured for (i) 1250 keV 60Co gamma rays, (ii) filtered X ray beams of average energies in the range 15-300 kVp, (iii) 147Pm beta electrons, (iv) thermal neutrons and (v) stopping alpha particles of initial energies in the range 0.5-5 MeV. A rapid decrease of TL efficiency with decreasing mean photon energy from ? = 1.04 ± 0.02 for 60Co, ? = 0.93 ± 0.02 for 300 kVp X rays to ? 0.59 ± 0.016 for 15 kVp X rays was observed. The measured value of relative efficiency for 147Pm beta electrons was ? = 0.90 ± 0.02. The relative efficiency for alpha particles decreased from ? = 0.06 ± 0.004 to ? = 0.03 ± 0.007 for particles of initial energies of 5 MeV and 1 MeV, respectively. The measured response of MCP-N detectors after doses of thermal neutrons was equal to 0.72 x 1010 Gy.n-1.cm2, which corresponds to ? = 0.10 ± 0.01. The efficiency for 2.73 MeV 3H tritons was found to be ? = 0.155 ± 0.02. The rapid decrease of sensitivity of LiF:Mg,Cu,P with increasing ionisation density is a microdosimetric effect, resulting from the saturation of the TL signal from high energy deposits. An empirical relationship between the mean lineal energy, yF, and ? has been found which can be used to predict the TL efficiency of MCP detectors for photons and electrons. However, TL efficiency ? is not a unique function of yF so this relationship cannot be used to predict the value of ? over the whole range of ionisation densities (LET) of heavy charged particles stopping in the detector.