  A nonperturbative theory of multiphonon anharmonic decay of strongly excited
local mode is developed whereby the mode is considered classically and phonons,
quantum mechanically. The decay rate of the mode is expressed via the negative
frequency parts of the phonon pair correlation functions. In the case of
two-phonon decay the later satisfy the linear integral equations while in the
case of two- and more-phonon decay they satisfy the nonlinear integral
equations. As a result, the processes mentioned differently depend on the mode
amplitude A: two-phonon processes smoothly deminish if A tends to infinity
while three- and more-phonon processes are fully switched-off at large
amplitudes and they abruptly switch-on if the amplitude approaches the critical
value. At that the decay rate gets rather high value (of the order of the mode
quantum per period). The final stage of the relaxation is well described by the
perturbation theory.
