In the atmospheric oxidation of organic compounds, free peroxy and oxy radicals play a crucial role. The traditional view is that peroxy radicals react with NO or with other (hydro-)peroxy radicals, whereas oxy radicals decompose, undergo a hydrogen shift, or react with O-2. However, we show in this quantum chemical and statistical-rate investigation that the presence of a double C=C bond in many (per)oxy radicals formed from isoprene and monoterpenes, the most abundant nonmethane hydrocarbons emitted into the atmosphere, can result in hitherto neglected ring-closure isomerizations. These processes are shown to be competitive under atmospheric conditions and can substantially alter the predicted oxidation products. As an illustration, the major pathways in the OH-initiated oxidation of beta-pinene are discussed. It is shown that the predominance of the (per)oxy ring-closure routes offers a consistent rationalization for the "anomalously" low observed yields of traditional-pathway oxidation products from this compound.