Interplay of quantum mechanical calculations and experimental data on hyperfine coupling constants of ethyl radical in zeolites at several temperatures was engaged to study the geometries and binding energies and to predict the temperature dependence of hyperfine splitting of a series of alkyl radicals in zeolites for the first time. The main focus is on the hyperfine interaction of alkyl radicals in the NaY and HY zeolites. The hyperfine splitting for neutral free radicals and free radical cations is predicted for different zeolite environments. This information can be used to establish the nature of the muoniated alkyl radicals in the NaY and HY zeolites via mu SR experiments. The ration hyperfine coupling constants of the ethane radical cation in these zeolites are very large with relatively little dependence on temperature. It was found that the intramolecular dynamics of alkyl free radicals are only weakly affected by their strong binding to zeolites. In contrast, the substrate binding has a significant effect on their intermolecular dynamics.