Exposure of polyethylene and paraffins to high-energy radiation produces main chain (transvinylene) unsaturation, and this rises to a maximum limiting concentration with increasing dose. On the other hand, vinyl unsaturation initially present diminishes on irradiation. Comparison of the effects of $\alpha$- and $\gamma$-irradiation of thin polyethylene films show that the initial G value for the formation of transvinylene unsaturation is not significantly affected by the l.e.t. of the radiation, but the maximum values reached differ by a factor of over 4. Similarly the decay of vinyl unsaturation is four times slower with $\alpha$-radiation. The destruction of unsaturation is ascribed to the reaction of H atoms liberated by radiation with the unsaturated groups acting as a scavenger. The difference between $\alpha$- and $\gamma$-radiation is due to an l.e.t. effect, more H atoms being available from radiation of lower l.e.t. Estimates are made of the proportion of H atoms which escape from the tracks of the two forms of radiation. The difference is much smaller than in the case of irradiated aqueous solutions. Data are also presented on the formation of carbonyl with $\alpha$- and $\gamma$-radiation, both in the presence of air, and during subsequent exposure.