Quantum chemical calculations are carried out to study the reaction of ethane with molecular oxygen in the ground triplet and singlet delta states. Transition states, intermediates, and possible products of the reaction on the triplet and singlet potential energy surfaces are identified on the basis of the coupled cluster method. The basis set dependence of coupled-cluster energy values is estimated by the second order perturbation theory. The values of energy barriers are also refined by using the compound CBS-Q and G3 techniques It was found that the C2H6 + O-2(X-3 Sigma(-)(g)) reaction leads to the formation of C2H5 and HO2 products, whereas the C2H6 + O-2(a(1)Delta(g)) process produces C2H4 and H2O2 molecules. The appropriate rate constants of these reaction paths are estimated on the basis of variational and nonvariational transition state theories assuming tunneling and possible nonadiabatic transitions in the temperature range 500-4000 K. The calculations showed that the rate constant of the C2H6 + O-2(a(1)Delta(g)) reaction path is much greater than that of the C2H6 + O-2(X-3 Sigma(-)(g)) one. At the same time, the singlet and triplet potential surface intersection is detected that leads to the appearance of the nonadiabatic quenching channel O-2(a(1)Delta(g)) + C2H6 -> O-2(X (3)Sigma(-)(g)) + C2H6. The rate constant of this process is estimated with the use of the Landau-Zener model. It is demonstrated that, in the case of the existence of thermal equilibrium in the distribution of molecules over the electronic states, at low temperatures (T < 1200 K) the main products of the reaction of C2H6 with O-2 are C2H4 and H2O2, rather than C2H5 and HO2. At higher temperature (T > 1200 K) the situation is inverted.