A theoretic analysis of magnon-induced damping &Ggr; of quasiparticle states in the normal phase of doped copper-oxide high-Tcmaterials is developed, based on a microscopic model which accounts for the specific2Dstructure of their electron and magnon spectra. Among the obtained energy and temperature dependencies of &Ggr; in different regimes, the most peculiar is the anomalously early onset of linear temperature dependence&Ggr;∝Twith a doping-independent coefficient. ©1998 American Institute of Physics.