Inferences of phylogenies and dates of divergence rely on accurate modeling of evolutionary processes; they may be confounded by variation in substitution rates among sites and changes in evolutionary processes over time. In vertebrate mitochondrial genomes, substitution rates are affected by a gradient along the genome of the time spent being single-stranded during replication, and different types of substitutions respond differently to this gradient. The gradient is controlled by biological factors including the rate of replication and functionality of repair mechanisms; little is known, however, about the consistency of the gradient over evolutionary time, or about how evolution of this gradient might affect phylogenetic analysis. Here, we evaluate the evolution of response to this gradient in complete primate mitochondrial genomes, focusing particularly on A-->G substitutions, which increase linearly with the gradient. We developed a methodology to evaluate the posterior probability densities of the response parameter space, and used likelihood ratio tests and mixture models with different numbers of classes to determine whether groups of genomes have evolved in a similar fashion. Substitution gradients usually evolve slowly in primates, but there have been at least two large evolutionary jumps: on the lineage leading to the great apes, and a convergent change on the lineage leading to baboons (Papio). There have also been possible convergences at deeper taxonomic levels, and different types of substitutions appear to evolve independently. The placements of the tarsier and the tree shrew within and in relation to primates may be incorrect because of convergence in these factors.