Bimolecular nucleophilic substitution (S N 2) reactions of allyl halogenides (Z–C αH 2–HC βC γH 2; Z=Halogen) and of respective substituted ketones (Z–C αH 2–RC βO RCH 3, C 2H 5, etc.) are comparatively studied using the semilocalized quantum-chemical approach suggested previously [J. Mol. Struct. (Theochem) 541 (2001) 1] and based on the power series for the one-electron density matrix [J. Mol. Struct. (Theochem) 343 (1995) 183]. Contributions of the direct (through-space) interaction between the electron-donating orbital of nucleophile and the electron-accepting orbital of the nucleofuge-containing (Z–C α) bond and of various indirect (through-bond) interactions between the same orbitals to the population acquired by the nucleofuge Z during the reaction process may be considered separately and explicitly in this approach. Moreover, orbitals of the nearest-neighborhood of the Z–C α bond play the role of the principal mediators in the indirect interactions. On this basis, the C βC γ and C βO bonds are compared in respect of mediating abilities of their π-orbitals in the above-mentioned indirect interactions and thereby of their contributions to relative rates of S N 2 processes. It is demonstrated that the indirect participation of the bonding π-orbital of the C βC γ bond contributes to lowering of the total population acquired by the nucleofuge Z owing to the nucleophilic attack and thereby of the relative reaction rate, whereas the increment of the antibonding orbital gives rise to an opposite effect. For highly electron-donating (soft) nucleophiles, the second contribution predominates over the first one, and this fact serves to account for the known higher reactivity of allyl halogenides as compared to respective alkyl halogenides. Furthermore, passing from the C βC γ to the C βO bond is shown to be accompanied by such changes in shapes and one-electron energies of bond orbitals that ensure a significant reduction of the absolute value of the negative increment of the bonding orbital and a simultaneous increase of the positive contribution of the antibonding orbital to the total population acquired by the nucleofuge. This principal result of the paper forms the basis for a new interpretation of the largely increased reactivity of α-halocarbonyl compounds vs. their hydrocarbon analogues in terms of direct and indirect interactions of bond orbitals.