The isothermal annealing experiments on synthetic hydroxyapatite and fossil tooth enamel samples show that the decay of its g=2.0018 line obeys the mixed first- and second-order annealing kinetics. The 2nd-order decay constant depends strongly on temperature and is roughly estimated to be about 10 -19 g/s for hydroxyapatite at 280℃. The effect of the 2nd-order annealing kinetics on ESR dating of ancient （early Pleistocene） fossil tooth enamel samples should be further studied.