The atmospheric degradation pathways of the atmospherically important terpenes a-pinene and beta -pinene are studied using density functional theory. We employ the correlation functional of Lee, Yang, and Parr and the three-parameter HF exchange functional of Becke (B3LYP) together with the 6-31G(d) basis set. The C-C bond scission reactions of the beta -hydroxyalkoxy radicals that are formed after OH addition to alpha -pinene and beta -pinene are investigated. Both of the alkoxy radicals formed from the alpha -pinene-OH adduct possess a single favored C-C scission pathway with an extremely low barrier (similar to3 kcal/mol) leading to the formation of pinonaldehyde. Neither of these pathways produces formaldehyde. and preliminary computational results offer some support for suggestions that 1,5 or 1,6 I-I-shift (isomerization) reactions of alkoxy radicals contribute to formaldehyde production. In the case of the alkoxy radical formed following OH addition to the methylene group of beta -pinene, there exists two C-C scission reactions with nearly identical barrier heights (similar to7.5 kcal/mol); one leads to known products (nopinone and formaldehyde) but the ultimate products of the competing reaction are unknown. The single C-C scission pathway of the ether alkoxy radical from beta -pinene possesses a very low (similar to4 kcal/mol) barrier. The kinetically favored C-C scission reactions of all four alkoxy radicals appear to be far faster than expected rates of reaction with O-2. The rearrangement of the alpha -pinene-OH adduct, a keg; step in the proposed mechanism of formation of acetone from alpha -pinene. is determined to possess a barrier of 11.6 kcal/mol. This value is consistent with another computational result and is broadly consistent with the modest acetone yields observed in product yield studies.