The influence of two-level tunnelling systems and``bosonic peakº on the second-order Doppler displacement of Mo È ssbauer g-radiation in disordered materials is investigated. It is shown, that the Mo È ssbauer frequency temperature displacement at temperatures 10 À4 K`T`w m " hak B is determined by``bosonic peakº and at T`10 À4 K by two-level tunnelling systems.