The effect of vibrational motion on resonant charge transport through single molecule junctions is investigated. The study is based on a combination of first-principles electronic structure calculations to characterize the system and inelastic scattering theory to calculate transport properties.The extension of the methodology to describe hole transport through occupied molecular orbitals is discussed. The methodology is applied to molecular junctions where a benzene molecule is connected via alkanethiolate bridges to two gold electrodes. The results demonstrate that, depending on the coupling between the electronic π-system of the benzene ring and the gold electrodes, vibronic coupling may have a significant influence on the transport properties of the molecular junction.Recent advances in experimental studies of single molecule conduction [1, 2, 3, 4,5,6,7,8,9] have stimulated great interest in the basic mechanisms which govern electron transport through nanoscale molecular junctions [10,11,12]. An interesting aspect that distinguishes molecular conductors from mesoscopic semiconductor devices is the possible influence of the nuclear degrees of freedom of the molecular bridge on electron transport. Due to the small size of molecules, the charging of the molecular bridge is often accompanied by significant changes of the nuclear geometry. The current-induced excitation of the vibrations of the molecule may result in heating of the molecular bridge and possibly breakage of the junction. Conformational changes of the geometry of the conducting molecule are possible mechanisms for switching behavior and negative differential resistance [13]. Furthermore, the observation of vibrational structures in conduction measurements allows the unambiguous identification of the molecular character of the current. Vibrational structures in molecular conductance were observed, for example, in electron transport experiments on H 2 , HD, and D 2 between platinum electrodes [14] using the mechanically controllable break junction technique. Thereby, changes in the conductance were assigned to switching between two different local geometrical configurations induced by the transverse motion of the molecule. The observed vibrational structures could be classified as longitudinal or transversal [15]. In studies of C 60 molecules between gold electrodes [2] the center of mass motion of the molecular bridge was observed. Other experiments on this system [16, 17] as well as on C 70 [7], (C 70 ) 2 [18], and copper phtalocyanin [6] on an aluminum oxide film showed structures which were related to the internal vibrational modes of the molecule. The aluminum oxide layer in the latter experiment acted as an insulating layer, which effectively reduces the electronic coupling between the molecule and the metal substrate thus facilitating the effect of vibrational motion on the conductance. In another STM experiment [19], pronounced progressions of vibrational modes were observed and the dependence of the vibronic coupling on the spatial position ...