The kinetics of exchange of adenine nucleotides in a system with reconstituted mitochondrial adenine nucleotide translocase (ANT) was simulated mathematically to analyze the basic mechanisms of ANT functioning. Two known alternative kinetic schemes were analyzed, the ping-pong type scheme with single-center substrate binding and the scheme of sequential two-center substrate binding at opposite sides of ANT. According to our modeling, both schemes can explain the experimental data on the adenine nucleotide exchange in the reconstituted ANT system. However, the characteristic kinetic pattern of ADP exchanges in the mono exchange mode was reproduced only by the sequential binding scheme. This scheme is consistent with the data on the tetrameric structure of ANT. On the other hand, only the single-center binding scheme was compatible with recent data on possible translocation of ATP and ADP by the carrier that has no bound adenine nucleotide on its opposite side. Based on the analysis of the literature data on ANT properties, a compromise scheme of ANT operation was proposed. In the framework of this scheme, the ANT dimers function by the single-center binding mechanism: however, in tetramers they are integrated into a substructure with two oppositely oriented binding centers working by the mechanism of sequential substrate binding. Labile bonds between the ANT-forming dimers could allow conformational rearrangements of ANT induced by various influences on mitochondrial membrane structure, including those leading to the induction of permeability transition pores in apoptosis.