Electron spin-lattice relaxation was measured by the electron spin echo method in a broad temperature range above 4.2 K for Cu(2+) ions and free radicals produced by ionizing radiation in triglycine sulfate (TGS) and Tutton salt (NH4)(2)Zn(SO4)2 ⋅ 6H2O crystals. Localization of the paramagnetic centres in the crystal unit cells was determined from continuous wave electron paramagnetic resonance spectra. Various spin relaxation processes and mechanisms are outlined. Cu(2+) ions relax fast via two-phonon Raman processes in both crystals involving the whole phonon spectrum of the host lattice. This relaxation is slightly slower for TGS where Cu(2+) ions are in the interstitial position. The ordinary Raman processes do not contribute to the radical relaxation which relaxes via the local phonon mode. The local mode lies within the acoustic phonon band for radicals in TGS but within the optical phonon range in (NH4)(2)Zn(SO4)2 ⋅ 6H2O. In the latter the cross-relaxation was considered. A lack of phonons around the radical molecules suggested a local crystal amorphisation produced by x- or γ-rays.