In this paper, we use a variety of mathematical techniques to explore existence, local stability, and global stability of equilibria in abstract models of mitochondrial metabolism. The class of models constructed is defined by the biochemical description of the system—an electron transport chain coupled to a process of charge translocation across a membrane. The conclusions are based on the reaction network structure, and we make minimal assumptions on the kinetics of the reactions involved. In the absence of charge translocation these models have previously been shown to behave in a very simple manner with a single, globally stable equilibrium. We show that with charge translocation the conclusion about a unique equilibrium remains true, but local and global stability do not necessarily follow. The length of the chains proves to be important: For short electron transport chains it is possible to make claims about local and global stability of the equilibrium which are no longer valid for longer chains. Some particular conditions which ensure stability of the equilibrium for chains of arbitrary length are presented.