The specific heat has been measured for the relaxor ferroelectrics PbMg_1/3Nb_2/3O₃ and PbMg_1/3Ta _2/3O₃ and the low-dielectric-constant material BaMg _1/3Ta_2/3O₃ over a temperature range of 2-420 K. The behaviours of the specific heat for PbMg_1/3Ta _2/3O₃ and BaMg_1/3Ta_2/3O₃ crystals have been qualitatively compared. A large excess of specific heat of PbMg_1/3Ta_2/3O₃ over that of BaMg _1/3Ta_2/3O₃ has been revealed. The behaviour of the low-temperature specific heat of PbMg_1/3Nb_2/3O ₃ has been analysed in the frameworks of the shell model, Debye model, Einstein oscillator, two-level systems approach, and fractal approach. The excess of the specific heat of PbMg_1/3Nb_2/3O ₃ over the harmonic phonon contribution has been estimated, and its possible origin is discussed.