The results of X-band electron spin resonance (ESR) and electron spin echo (ESE) measurements for free radicals generated in Cd(HCOO)2·2H2O single crystal are presented. From ESR spectra analysis the radicals were identified as CO2(-) after x-ray irradiation and as HOCO after γ-ray irradiation. The room temperature g-factors are: g|| = 1.9969 and g⊥ = 2.0024 for CO2(-) and g1 = 2.0087, g2 = 2.0029 and g3 = 1.9960 for HOCO. Axial g-tensor symmetry for CO2(-) is due to fast reorientation of the radical molecule around the g||-axis. Assignment of HOCO is confirmed by hyperfine splitting (Amax = 0.4 mT) from a single distant proton. Spin lattice relaxation rate was determined from ESE measurements in temperature range 4-250 K. Both radicals relax via local resonance mode lying within acoustic phonon branch. The existing theories of electron spin-lattice relaxation via local resonance mode are critically reviewed and compared with experimental data. A new approximation is proposed giving local mode energy ħω(R) = 56 cm(-1) for CO2(-) and ħω(R) = 44 cm(-1) for the HOCO-radical.