Mitochondria incubated aerobically in the presence of tetrapropylammonium and weak acids and in the presence of trace amounts of tetraphenylboron undergo a series of damped oscillations reflecting cycles of osmotic swelling and shrinkage. The matrix volume changes are consequent to transport of tetrapropylammonium catalytically stimulated by tetraphenylboron. The amplitude and frequency of the oscillations increase with the concentration of tetrapropylammonium, as required for critical rates and extents of ion influx. Addition of bovine serum albumin abolishes both the uptake of tetrapropylammonium and the oscillations. Volume oscillations are paralleled by cyclic activation and depression of the respiratory rate. Two lines of evidence suggest that the train of damped oscillations depends on the cyclic activation of an electroneutral exchange of H+ with organic cations rather than on cyclic uncoupling. First, further increase of cation permeability due to a pulse of tetraphenylboron, after initiation of cation efflux, restores cation influx. Second, addition of Mg2+, which abolishes the oscillations, has a much more marked inhibitory effect on the process of cation efflux than on cation influx. Conversely, addition of A23187, which removes membrane-bound Mg2+, promotes cation efflux and thus the oscillations. It is suggested that, in the present system, stretching of the inner membrane and Mg2+ depletion result in activation of an electroneutral H+/organic cation exchange, and that cyclic activation of this reaction results in damped oscillations.