Quantum mechanical calculations were used to determine the structure and stability of second-generation peroxy and alkoxy radicals formed in the atmospheric degradation of isoprene (2-methyl-1,3-butadiene). Certain of these radicals exhibit a novel hydrogen bonding motif, consisting of two intramolecular hydrogen bonds. The hydrogen bonds are donated in series, with an enol group donating a hydrogen bond to a -CH2OH group, which donates in turn to the oxygen radical center. This hydrogen bonding motif opens a new reaction pathway: the simultaneous transfer of two H-atoms across the hydrogen bonds with a barrier of only similar to5 kcal/mol in the alkoxy radicals, but similar to20 kcal/mol in the peroxy radicals. Rate constants for these reactions were calculated, and the effects of tunneling on the rate constant were examined. All species and reactions were analyzed at the B3LYP/6-311G(2df,2p) level of theory; the transition states for the double H-atom transfer reactions were also studied using the MPW1K functional and the CBS-QB3 method. Similar chemistry is possible for alkoxy and peroxy radicals derived from other volatile organic compounds of atmospheric interest.