Monoterpenes are a group of volatile organic compounds (VOCs) emitted to the atmosphere in large amounts. Studies have linked the autoxidation of monoterpenes to the formation of secondary organic aerosols, which impact Earth's climate and human health. Here, we study the hydroxy peroxy radicals formed by OH- and O-2-addition to the six atmospherically relevant monoterpenes alpha-pinene, beta-pinene, Delta(3)-carene, camphene, limonene, and terpinolene. The six monoterpenes all have a sixmembered ring but differ in the binding pattern of the four remaining carbon atoms and the position of the double bond(s). We use a multiconformer transition state theory approach to calculate the rate coefficients of the peroxy radical hydrogen-shift (H-shift) and endoperoxide formation reactions of these peroxy radicals. Our results suggest that primarily the isomers with a carbon-carbon double bond remaining after OH- and O-2-addition undergo unimolecular reactions with rate coefficients large enough to be of atmospheric importance. This greatly limits the number of potentially important unimolecular pathways. Specifically, we find that the ring-opened alpha- and beta-pinene isomers as well as isomers of limonene and terpinolene have unimolecular reactions that are fast enough to likely dominate their reactivity under most atmospheric conditions.