In this work we analyze the onset and manifestation of irreversibility phenomena in the charge transport at single and double metal-redox molecule interfaces, with special emphasis on the role of the nuclear system reorganization energy in causing the distortion of cyclic voltammograms in the first case and the occurrence of hysteresis phenomena in the second case. Under physical conditions for which two states of the molecular system come into play, effects of irreversibility increase with the reorganization energy at a single interface, while an opposite trend is seen in the conduction through a molecular junction. The apparent contradiction between these two behaviors, which was raised in a previous work (Migliore, A.; Nitzan, A., J. Am. Chem. Soc. 2013, 135, 9420-32) is here resolved through detailed investigation of the connections between molecule reorganization energy, bias-dependent population of the molecular redox site(s), and threshold voltage scan rate for the onset of irreversible behavior. Moreover, our investigation of the effects of the reorganization energy on the voltammogram peaks proposes a strategy for extracting the value of the reorganization energy of the molecular system from the experimental behavior. (C) 2015 Elsevier Ltd. All rights reserved.