Under the influence of tritium $\beta $-radiation, dissolved trans-cyclohexane-1,2-diol exchanges carbon-bound hydrogen with the solvent (tritiated water). The exchange occurs not only at the hydroxyl-substituted $(\alpha)$ carbon atoms but also at non-$\alpha $ positions, which are, on the average, less reactive. The overall $G$-value for exchange in all positions is $ca$. 0.33. With $\gamma $-irradiation, exchange takes place with a slightly lower overall $G$-value. Exchange at $\alpha $-positions occurs with predominant retention of configuration (76%). In the corresponding $\alpha $-exchange of cis-cyclohexane-1,2-diol, 79% of the reaction proceeds with inversion, i.e. the labelled products are in both reactions formed in practically the same ratio (trans-diol: cis-diol $\simeq $ 3.5:1). It is concluded that the reactions go through a common intermediate (or rapidly equilibrating common set of intermediates), for both diols as substrates. A chemically reasonable mechanism in accordance with this requirement involves as the first step hydrogen abstraction (mainly by hydroxyl radicals) from a C--H grouping, followed by conversion of the organic radical produced to the carbanion by electron capture. The carbanion then reverts to a diol by protonation (tritonation). Equilibration of diastereomers can occur in the radical and/or in the carbanion. The involvement of both the hydroxyl radical and the solvated electron is qualitatively in accord with the action of electron and radical scavengers on the velocity of the exchange reaction.