A method of time-dependent self-consistent phonons is applied for a nonperturbative description of the relaxation of a local mode caused by multiphonon anharmonic transitions between its vibrational levels. Theory predicts a sharp change of the relaxation law at the critical vibrational level. In the vicinity of this level the rates of the transitions attain a very high value, comparable to the dephasing rate of phonons. In the case of weak interactions, the results agree with perturbation theory. (C) 2001 American Institute of Physics.