DFT B3LYP calculations with the 6-31G(d,p), 6-311G(d,p), 6-311 +G(d,p), and 6-311++G(d,p) basis sets were carried out to explore the mechanisms of the CH + O-2(X(3)Sigma(g)(-)) --> CO2 + H (1) and CH + O-2(X(3)Sigma(g)(-)) --> CO + OH (2) reactions. On the basis of the calculated reaction paths, the two reaction channels are predicted to occur via the following reaction steps. The CH radical initially attacks one of the O atoms of the O-2(3Sigma(g)(-)) molecule, leading to an intermediate HCOO (IM1, (2)A'), followed by formation of a bond between the C atom and the distal O atom in IM1, leading to an nonplanar structure (intermediate IM2) having a COO ring. The rupture of the O-O bond in IM2 leads to the formyloxyl radical (HCO2, planar) in its B-2(2) state (IM3a). The B-2(2) formyloxyl radical (IM3a) can be easily converted into the (2)A(1) formyloxyl radical (IM3b) via either a transition state ((2)A') or crossing of the B-2(2) and (2)A(1) potential energy surfaces. The final products of reaction channels 1 and 2 are obtained from IM3b via trivial chemical processes: (i) for channel 1, an H dissociation process and (ii) for channel 2, H migration from the C center to one of the two O centers leading to an intermediate (OCOH, IM4), followed by cleavage of the central C-O bond in IM4. All these reaction steps have transitions states except the initial step and the step from IM4 to CO + OH. The energies of all the transition states, all the intermediates, the (2)A(1)-B-2(2) crossing region, and the final products are lower or much lower than that of the reactants, which indicates that reaction channels I and 2 are energetically feasible. The energy levels, structures, and characteristics of the three a states ((2)A(1), B-2(2), and (2)A') of the formyloxyl radical were carefully studied at the B3LYP levels, and the results are compared with previous theoretical results. The initial attack via the least-motion approach (insertion of CH into O-2 directly, leading to IM3b) was examined, but the calculations imply that it is not feasible. The CASSCF and CASPT2 methods were also attempted for the reaction path calculations. It has been noted that quantitatively reliable CAS calculations for these radical reactions would be technically difficult to make at the present stage.