Development of a technique for determining the concentration of alkyl radicals trapped in irradiated polyethylene using radio-iodine is described. It is applied to study the kinetics of alkyl radical disappearance in irradiated polyethylene and polypropylene, and the kinetics are interpreted in terms of a simple model. The radicals are assumed to be formed in isolated spherical spurs and rapidly attain an approximately uniform concentration within a spur. This concentration decreases with time due to second-order recombination accompanied by a diffusion-like expansion of the spur. Recombination is increased by hydrogen and the diffusive expansion is increased by hydrogen and by preirradiation. Both processes are faster in polypropylene than in polyethylene. The number of free radicals per spur after the irradiation decreases with increase in radiation dose due probably to the effect of the hydrogen produced by irradiation.