The influence of molecular structure (branched vs linear) on product formation in the heterogeneous oxidation of unsaturated organic aerosol is investigated. Particle phase product isomers formed from the reaction of squalene (C30H50, a branched alkene with six C=C double bonds) and linolenic acid (C18H30O2, a linear carboxylic acid with three C-C double bonds) with OH radicals are identified and quantified using two-dimensional gas chromatography-mass spectrometry. The reactions are measured at low and high [O-2] (similar to 1% vs 10% [O-2]) to understand the roles of hydroxyalkyl and hydroxyperoxy radical intermediates in product formation. A key reaction step is OH addition to a C-C double bond to form a hydroxyalkyl radical. In addition, allylic alkyl radicals, formed from H atom abstraction reactions by hydroxyalkyl or OH radicals play important roles in the chemistry of product formation. Functionalization products dominate the squalene reaction at similar to 1% [O-2], with the total abundance of observed functionalization products being approximately equal to the fragmentation products at 10% [O-2]. The large abundance of squalene fragmentation products at 10% [O-2] is attributed to the formation and dissociation of tertiary hydroxyalkoxy radical intermediates. For linolenic acid aerosol, the formation of functionalization products dominates the reaction at both similar to 1% and 10% [O-2], suggesting that the formation and dissociation of secondary hydroxyalkoxy radicals are minor reaction channels for linear molecules. The distribution of linolenic acid functionalization products depends upon [O-2], indicating that O-2 controls the reaction pathways of the secondary hydroxyalkyl radical. For both reactions, alcohols are formed in favor of carbonyl functional groups, suggesting that there are some key differences between heterogeneous reactions involving allylic radical intermediates and those reactions of OH radicals with simple saturated hydrocarbons.