The method used in Ref. [3] to treat the magnetic susceptibility of the coupled system was extended to analyse the spin-lattice relaxation processes. In the case of weak coupling, the detailed expressions for the line shape of longitudinal nonresonance absorption and transverse resonance absorption were obtained by solving a set of coupled equations. The longitudinal and transverse relaxation times have been obtained as functions of the external alternating field. This is the direct consequence of the fact that the equations we used are of the non-Markovian type. Far away from the resonance point, the actual expression of the line shape is found to be quite different from that of the Debye or Lorentz type; the non-Markovian effect generally can not be ignored.In the case of S = 1, all the processes involved in the expressions of longitudinal and transverse relaxation times were systematically analysed. It is found that some terms correspond to the usually discussed processes such as one phonon process; the Orbach process, etc., but involve the frequency as a parameter as mentioned above. The influence of lifetime of phonons on the transverse spin-lattice relaxation was also discussed.