Potential energy surfaces (PESs) of the reactions of 1- and 2-naphthyl radicals with molecular oxygen have been investigated at the G3(MP2,CC)//B3LYP/6-311G** level of theory. Both reactions are shown to be initiated by barrierless addition of O(2) to the respective radical sites of C(10)H(7). The end-on O(2) addition leading to 1- and 2-naphthylperoxy radicals exothermic by 45-46 kcal/mol is found to be more preferable thermodynamically than the side-on addition. At the subsequent reaction step, the chemically activated 1- and 2-C(10)H(7)OO adducts can eliminate an oxygen atom leading to the formation of 1- and 2-naphthoxy radical products, respectively, which in turn can undergo unimolecular decomposition producing indenyl radical + CO via the barriers of 57.8 and 48.3 kcal/mol and with total reaction endothermicities of 14.5 and 10.2 kcal/mol, respectively. Alternatively, the initial reaction adducts can feature an oxygen atom insertion into the attacked C(6) ring leading to bicyclic intermediates a10 and a10' (from 1-naphthyl + O(2)) or b10 and b10' (from 2-naphthyl + O(2)) composed from two fused six-member C(6) and seven-member C(6)O rings. Next, a10 and a10' are predicted to decompose to C(9)H(7) (indenyl) + CO(2), 1,2-C(10)H(6)O(2) (1,2-naphthoquinone) + H, and 1-C(9)H(7)O (1-benzopyranyl) + CO, whereas b10 and b10' would dissociate to C(9)H(7) (indenyl) + CO(2), 2-C(9)H(7)O (2-benzopyranyl) + CO, and 1,2-C(10)H(6)O(2) (1,2-naphthoquinone) + H. On the basis of this, the 1-naphthyl + O(2) reaction is concluded to form the following products (with the overall reaction energies given in parentheses): 1-naphthoxy + O (-15.5 kcal/mol), indenyl + CO(2) (-123.9 kcal/mol), 1-benzopyranyl + CO (-97.2 kcal/mol), and 1,2-naphthoquinone + H (-63.5 kcal/mol). The 2-naphthyl + O(2) reaction is predicted to produce 2-naphthoxy + O (-10.9 kcal/mol), indenyl + CO(2) (-123.7 kcal/mol), 2-benzopyranyl + CO (-90.7 kcal/mol), and 1,2-naphthoquinone + H (-63.2 kcal/mol). Simplified kinetic calculations using transition-state theory computed rate constants at the high-pressure limit indicate that the C(10)H(7)O + O product channels are favored at high temperatures, while the irreversible oxygen atom insertion first leading to the a10 and a10' or b10 and b10' intermediates and then to their various decomposition products is preferable at lower temperatures. Among the decomposition products, indenyl + CO(2) are always most favorable at lower temperatures, but the others, 1,2-C(10)H(6)O(2) (1,2-naphthoquinone) + H (from a10 and b10'), 1-C(9)H(7)O (1-benzopyranyl) + CO (from a10'), and 2-C(10)H(7)O (2-benzopyranyl) + O (from b10 and minor from b10'), may notably contribute or even become major products at higher temperatures.