We have applied the dynamical jellium model for metal clusters, which treat
s simultaneously the vibrational modes of the ionic jellium background in a
cluster, the quantized electron motion and the interaction between the ele
ctronic and the ionic subsystems beyond the adiabatic approximation, for th
e calculation of widths of electron excitations in metal clusters caused by
multiphonon transitions, and investigated their temperature dependences. W
e have also estimated the decay time and the energy relaxation time of elec
tron excitations in metal clusters.