The cyclic voltammetry of UQ((10)) and PQ((9)) incorporated in a supported lipid bilayer and reacting at a gold electrode is quantitatively analyzed assuming that the electrochemical process consists of a nine-member square scheme and using the approach developed earlier by Laviron. The striking change affecting the shape of the cathodic peak in the cyclic voltammograms when pH is increased from less than 7.5 to higher values reflects a shift from kinetic control of the cathodic process by the equivalent first electron exchange to kinetic control by the equivalent second electron exchange. Reasonable values are found for the thermodynamic and kinetic characteristics of the electrochemical process.