Multireference quantum chemical research with the aid of complete active space self-consistent field approach was performed to study the elementary reactions of CH4 with O-2 in a(1)Delta(g), b(1)Sigma(+)(g), c(1)Sigma(-)(u), and A('3)Delta(u) electronically excited states highly relevant for plasma-assisted combustion and for plasma-chemical fuel reforming. The thermodynamically and kinetically favorable reaction pathways and likely intersystem crossings for the first step of the methane oxidation have been found out. The key energy values were refined based upon the extended multiconfiguration quasi-degenerate 2nd-order perturbation theory. It has been exhibited that the reaction of O-2(a(1)Delta(g)) and O-2(A('3)Delta(u)) with CH4 proceeds through the abstraction of hydrogen with fairly low energy barriers that led to the formation of the HO2 molecule in (2)A '' and (2)A' electronic states, respectively. These results were compared with the findings of previous theoretical investigations. The oxygen molecule in singlet sigma b state was evinced to be nonreactive with regard to the methane. However, for c(1)Sigma(-)(u) state, the reactive interaction was nevertheless found possible due to the significant probability of the nonadiabatic transitions. Appropriate thermal rate constants for revealed channels have been calculated employing variational transition-state theory and capture approximation. Corresponding three-parameter Arrhenius expressions for the broad temperature range (T = 300-3000 K) were reported.