This theoretical study focuses on two indole derivatives, melatonin (1) and carvedilol (8), with the objective of improving our understanding of the molecular mechanisms underlying their radical-scavenging activity. Quantum-mechanical calculations were carried out using the AM1 semi-empirical method, some results being confirmed by ab initio (3-21G) calculations. The quantum-chemical descriptor Δ Hox (relative adiabatic oxidation potential) and the shape of the SOMO (singly occupied molecular orbital) indicate that the stabilization of its radical cation can partially explain the well-documented antioxidant efficacy of melatonin. This stablization may result from electrostatic interactions and from a hyperconjugative effect existing in a family of conformers of the melatonin radical cation having the side chain almost perpendicular to the plane of the aromatic rings. Furthermore, 6-hydroxymelatonin (7) appears to be a better free-radical scavenger than melatonin (1) in agreement with experimental results. According to the theoretical parameters Δ Hox and Δ Habs (relative bond dissociation enthalpy), carvedilol (8) is not a good antioxidant, in contrast to its ring-hydroxylated metabolites whose powerful antioxidant effects are explained by the formation of an oxyl radical stabilized by delocalization over the carbazole nucleus.