Charged electrochemical capacitors and battery electrodes are in a state of high Gibbs energy in relation to that of their discharged states; hence there is a thermodynamic “driving force” for their self-discharge on open-circuit. Several mechanisms for self-discharge can be envisaged and diagnostically distinguished. They must take place by mixed cathodic/anodic electrochemical processes (as in corrosion) or, in some cases, by a surface-chemical process. Self-discharge can be characterized by two procedures: (a) measurement of open-circuit decline of electrode potential or state-of-charge with time or (b) by establishing the polarizing currents, so-called float-currents, at various potentials in the self-discharge process that are required just to maintain those respective potentials constant. The importance, for either case, of characterizing the self-discharge behavior individually for each electrode of a cell pair (using a third electrode as a reference) is stressed. Experimental data are presented for potentiostatic float-current measurements at porous C-cloth and glassy-C electrodes, and related to digital potential-decay measurements under the same conditions in aqueous H2SO4 below the decomposition potential of the solution. Treatment of an equivalent circuit model enables the time dependence of components of double-layer charging and self-discharge under potentiostatic float conditions to be understood and evaluated.