There is a pressing need to identify and monitor reaction intermediates in water at high temperatures and pressures, but conventional techniques have limited capability for studying transient free radicals under such challenging conditions. Apparatus has now been developed to permit muon avoided-level crossing spectroscopy (mu LCR) of organic free radicals in superheated water. The combination of mu LCR with transverse-field muon spin rotation (TF-mu SR)provides the means to identify and characterize free radicals via their nuclear hyperfine coupling constants. Because the radicals are derived from the addition of muonium (Mu = mu(+)e(-)) to unsaturated compounds, the ensuing muoniated free radicals correspond to conventional organic free radicals but with a muon spin label substituted for one of the protons. Muon spin spectroscopy is the only technique presently being used to characterize transient free radicals under hydrothermal conditions in an unambiguous manner, free from interference from other reaction intermediates. This paper demonstrates how muoniated radicals can be used to monitor the species present in hydrothermal systems, and examples are presented from two classes of reaction: dehydration of alcohols and enolization of ketones. Spectra are displayed and hyperfine constants reported for muoniated forms of the following free radicals in superheated water (typically 350 degrees C at 250 bar): 2-propyl, 2-methyl-2-propyl (tert-butyl), and 2-hydroxy-2-propyl. The latter radical is the product of muonium addition to both the keto and the enol forms of acetone, but different isotopomers are produced according to which reaction channel is dominant. This should prove invaluable in future studies of the role of enols in combustion.