The activity of polymerase γ is complicated, involving both correct and incorrect DNA polymerization events, exonuclease activity, and the disassociation of the polymerase:DNA complex. Pausing of pol-γ might increase the chance of deletion and depletion of mitochondrial DNA. We have developed a stochastic simulation of pol-γ that models its activities on the level of individual nucleotides for the replication of mtDNA. This method gives us insights into the pausing of two pol-γ variants: the A467T substitution that causes PEO and Alpers syndrome, and the exonuclease deficient pol-γ (exo(-)) in premature aging mouse models. To measure the pausing, we analyzed simulation results for the longest time for the polymerase to move forward one nucleotide along the DNA strand. Our model of the exo(-) polymerase had extremely long pauses, with a 30 to 300-fold increase in the time required for the longest single forward step compared to the wild-type, while the naturally occurring A467T variant showed at most a doubling in the length of the pauses compared to the wild-type. We identified the cause of these differences in the polymerase pausing time to be the number of disassociations occurring in each forward step of the polymerase.