Very little is known about the behavior of free H atoms and small organic radicals inside clathrate hydrate structures despite the relevance of such species to combustion of hydrocarbon hydrates. Muonium is an H atom analog, essentially a light isotope of hydrogen, and can be used to probe the chemistry of H atoms and transient free radicals. We demonstrate the first application of muon spin spectroscopy to characterize radicals in clathrate hydrates. Atomic muonium was detected in hydrates of cyclopentane and tetrahydrofuran, and muoniated free radicals were detected in the hydrates of cyclopentene and 2,5-dihydrofuran, indicating rapid addition of muonium to the organic guest. Muon avoided level-crossing spectra of the radicals in hydrates are markedly different to those of the same radicals in pure organic liquids at the same temperature, and this can be explained by limited mobility of the enclathrated radicals, leading to anisotropy in the hyperfine interactions.