Exposure of sodium dithionate to ⁶⁰Co γ-rays at 77 K gives a centre having hyperfine coupling to ³³S (A_∥= 165 G, A_⊥= 135 G) which is thought to be the primary electron-capture centre [S₂O₆]^3– having the extra electron confined to the S–S σ* orbital. This assignment is supported by the observation that ³³S features characteristic of [³³SO₃]^– radicals grew in as those assigned to [S₂O₆]^3– anions were lost on annealing. The major electron-loss centre is identified as the hydroxyl radical formed from hydrate water molecules. Sodium thiosulphate gives a radical having a large isotropic hyperfine coupling to ³³S. This centre, previously thought to be [S₂O₃]^–, is now identified as [S₂O₃]^3–. In anhydrous Na₂[S₂O₃] this centre exhibits hyperfine coupling to ²³Na. This salt and K₂[S₂O₃]·5H₂O give a new species having one very high g value, identified as [S₂O₃]^–. Two sets of ³³S features are obtained from [S₂O₆]^3– suggesting an asymmetric environment. In accord with this, two slightly different [˙SO₃]^– radicals are obtained on annealing. The anion [O₃SS–SSO₃]^3– is a primary product in irradiated sodium tetrathionate, but is not detected in thiosulphate even after annealing. A second centre formed from tetrathionate exhibits a large g value variation and extra hyperfine coupling to ²³Na.