The structures of the free radicals formed by the irradiation of potassium dithionate (K2S2O6) with 60Co γ-rays and 14N7+ ions were investigated by EPR to further examine a recently proposed LET effect in this material. Two types of SO3− radical ions were identified in X-irradiated single crystals by measurements at X- and Q bands. One of these (S1) exhibited 33S hyperfine couplings A⊥ = 12.49, A|| = 15.60 mT, the other (S2) A⊥ = 11.29, A|| = 13.92 mT. The g-factors were nearly isotropic, g⊥ = 2.0010, g|| = 2.0003; and g⊥ = 2.0026, g|| = 2.0008, respectively. The 33S hyperfine coupling tensors and g-tensors were axially symmetric about the trigonal <c>-axis, coinciding with the direction of the S–S bonds of the two non-equivalent S2O62− ions in the crystal. A model for the radiation damage was proposed in which the SO3− radical ions retain the orientation of the SO3 groups, aligned along the trigonal axis. The structure of a third main radical species (S3) with g⊥ = 2.0026, g|| = 2.0052 could not be unambiguously assigned, due to undetected 33S features. The relative integrated intensities of S1, S2 and S3 depended on the radiation quality and were approximately estimated as 0.18: 0.65:0.17 for 60Co γ-rays and 0.47: 0.38: 0.15 for 14N7+ ions. Additional weak lines on the low field side of the main signal were tentatively attributed to SO2− radical ions. An even weaker strongly anisotropic pair of lines was attributed to SO3− radical pairs separated by 0.93–0.95 nm along the trigonal axis.