Comprehensive quantum chemical analysis with the usage of density functional theory and post-Hartree Fock approaches were carried out to study the processes in the N-2(A(3)Sigma(+)(u)) + CH4 and N-2(A(3)Sigma(+)(u)) + C2H6 systems. The energetically favorable reaction pathways have been revealed on the basis of the examination of potential energy surfaces. It has been shown that the reactions N-2(A(3)Sigma(+)(u)) + CH4 and N-2(A(3 Sigma u)(+)) + C2H6 occur with very small or even zero activation barriers and, primarily, lead to the formation of N2H + CH3 and N2H + C2H5 products, respectively. Further, the interaction of these species can give rise the ground state N-2(X)(I)g(+)) and CH4 (or C2H6) products, i.e., quenching of N-2(A(3)Z(u)(+)) by CH4 and C2H6 molecules is the complex two-step process. The possibility of dissociative quenching in the course of the interaction of N-2(A(3)Eu+) with CH4 and C2H6 molecules has been analyzed on the basis of RRKM theory. It has been revealed that, for the reaction of N-2(A(3)E(u)(+)) with CH4, the dissociative quenching channel could occur with rather high probability, whereas in the N-2(A(3)E(u)(+)) + C2F16 reacting system, an analogous process was little probable. Appropriate rate constants for revealed reaction channels have been estimated by using a canonical variational theory and capture approximation. The estimations showed that the rate constant of the N-2(A(3)Z.+) + C2H6 reaction path is considerably greater than that for the N-2(A5Zu+) + CH4 one.