The paper provides a comprehensive, compatible and consistent approach to thermodynamics of electrolytic redox and non-redox systems, referred to aqueous, non-aqueous and mixed-solvent media. It is stated that the linear combination 2.f(O) - f(H) of elemental balances: f(H) for H and f(O) for 0 is the property distinguishing between redox and non-redox electrolytic systems. Namely, 2.f(O) - f(H) is the linear combination of concentration balances for other components of a non-redox system, of any degree of complexity. It is also proved that 2.f(O) - (H) is an independent equation when referred to a redox system, of any degree of complexity. The linear combination 2.f(O) - f(H) is a primary form, pr-GEB, of the Generalized Electron Balance (GEB), 2.f(O) - 1(H) = pr-GEB, named as the Approach II, and considered as the alternative for the Approach I to GEB, based on the "card game" principle. The equivalency of both approaches to GEB is also proved in this paper. The GEB, considered as a relatively new Law of Nature, is perceived as a turning point in the theory of electrolytic redox systems. (C) 2013 Elsevier Ltd. All rights reserved.