The reaction systems tert-butyl radical + O-2 isobutene + HO2, isobutene + OH, and isobutene-OH adducts + O-2, which are important to understanding the oxidation chemistry of tertiary butyl radical (C3C.) are analyzed. Thermochemical parameters are determined by ab initio-Moller-Plesset (MP2(full)/6-31 g(d)), complete basis set model chemistry (CBS-4 and CBS-q with MP2(full)/6-31g(d) and B3LYP/6-31g(d) optimized geometries), density functional (B3LYP/6-31g(d)), semiempirical MOPAC (PM3) molecular orbital calculations, and by group additivity estimation. Thermochemical kinetic parameters are developed for each elementary reaction path in these complex systems, and a chemical activation kinetic analysis using quantum Rice-Ramsperger-Kassel (QRRK) theory for k(E) and master equation analysis for falloff Is used to calculate rate constants as a function of pressure and temperature. An elementary reaction mechanism is constructed to model experimental data for oxidation of tert-butyl radical. Calculations for loss of tert-butyl precursor, 2,2,3,3-tetramethylbutane (C3CCC3), and production of isobutene and 2,2-dimethyloxirane from the mechanism are compared with experimental data reported in the literature. Reaction of tert-butyl radical (C3C.) with O-2 forms an energized tert-butyl peroxy adduct C3COO.* which can dissociate back to reactants, dissociate to isobutene + HO2, or isomerize to tert-butyl hydroperoxide ((C3COOH)-C-.). This isomer can dissociate to either isobutene + HO2 or 2,2-dimethyloxirane + OH, before it is stabilized. In the tert-butyl radical + O-2 reaction system, dissociation of the [C3COO.]* adduct to isobutene + HO2 via HO2 molecular elimination is faster than the hydrogen shift to (C3COOH)-C-. by a factor of 86:1 st 773 K and 60 Torr. The reaction barrier (reaction enthalpy difference between TS4 and (C3COOH)-C-.) for the (C3COOH)-C-. reaction to 2,2-dimethyloxirane + OH is calculated as 17.98 (19.06) kcal/mol at the CBS-q//MP2(full)/6-31g(d) level but is evaluated as 15.58 (18.06) kcal/mol by fitting experimental data. Data in parentheses are thermodynamic properties based on CBS-q//B3LYP/6-31g(d) calculation. Barriers for reactions of HO2 + isobutene --> (C3COOH)-C-. (HO2 addition at CD/C2 carbon atom of isobutene, CD = carbon double bond) and HO2 --> isobutene --> (C2CCOOH)-C-. (HO2 addition at CD/H2 carbon atom of isobutene) are respectively determined as 7.74 (7.38) and 10.69 (10.82) kcal/mol. 2,2-Dimethyloxirane is formed primarily by HO2 addition to isobutene. OH addition to isobutene results in adducts which further react with O-2 to form acetone, formaldehyde, and the OH radical (Waddington mechanism) with these pathways also analyzed.