Mitochondria are known to possess a rapid calcium uptake mechanism or uniport and both sodium-dependent and sodium-independent efflux mechanisms. Whether sodium-independent calcium efflux is mediated and whether sodium-dependent calcium efflux can be found in liver mitochondria have been questioned. Kinetics results relevant to the answers of these questions are discussed below. A slow, mediated, sodium-independent calcium efflux mechanism is identified which shows second order kinetics. This mechanism, which shows "nonessential activation" kinetics, has a Vmax around 1.2 nmol calcium per mg protein per min and a half maximal velocity around 8.4 nmol calcium per mg protein. A slow, sodium-dependent calcium efflux mechanism is identified, which is first order in calcium and second order in sodium. This mechanism has a Vmax around 2.6 nmol of calcium per mg protein per min. The sodium dependence is half saturated at an external sodium concentration of 9.4 mM, and the calcium dependence is half saturated at an internal calcium concentration of 8.1 nmol calcium per mg protein. The cooperativity of the sodium dependence effectively permits a terreactant system to be fit by a bireactant model in which [Na] only appears as the square of [Na]. This liver system shows simultaneous, as opposed to ping-pong, kinetics. It is also found to be sensitive to inhibition by tetraphenyl phosphonium, magnesium, and ruthenium red. A model is proposed in which mitochondrial calcium transport could function to "shape the pulses" of cytosolic calcium. Simultaneously, mitochondria may mediate a "calcium memory" coupled perhaps to activation of cytosolic events through calmodulin or perhaps to activation of electron transport through the activation of specific dehydrogenases by intramitochondrial calcium.