Alkyl cyclohexanes are a key component in novel biodiesel and jet fuel, which are of central focus to next-generation strategies for low-temperature combustion. The state-of-the-art chemical kinetics approach has been employed in the reaction of an oxygen molecule to the three isomers of 1,4-dimethylcyclohexyl radicals (cy-C8H15) to predict the temperature- and pressure-dependent branching ratios. The reaction energies were computed using quantum composite methods, i.e., CBS-QB3 and rate constants, and branching was calculated using Rice-Ramsperger-Kassel-Marcus (RRKM)/master equation (ME) simulations in the temperature range of 400 to 1000 K and pressure range of 0.001 to 100 bar. The RRKM/ME simulation reveals the addition of O2 to the primary radical, cy-C8H15 + O2 reaction (ROO-1), the formation of five-membered cyclic ether P7p (4-methyl-6-oxabicyclo[3.2.1]octane) and six-membered cyclic ether P10p (1-methyl-2-oxabicyclo[2.2.2]octane) are highly pressure-dependent below 0.01 bar and kinetically favorable pathway < 700 K. For tertiary cy-C8H15 + O2 (ROO-2), the formation of P5t (1,4-dimethyl-6-oxabicyclo[3.1.1]heptane), and P8t (1-methoxy-1,4-dimethylcyclohexane) are highly pressure-dependent and kinetically favorable pathway in the temperature range of 600 K to 750 K. On secondary cy-C8H15 + O2 (ROO-3) reaction, the formation of P4s (1,4-dimethyl-6-oxabicyclo[3.1.1]heptane), and P6s (1,4-dimethyl-7-oxabicyclo[4.1.0]heptane) competes with the stabilization of ROO-3 at a pressure lower than 0.01 bar. The updated energies and rate constants may also serve as general prototypes for low-temperature oxidation of alkyl cyclohexanes of next-generation fuels such as bisabolane and jet fuel.