During the last decades, the mammalian genome has been proposed to have regions prone to breakage and reorganization concentrated in certain chromosomal bands that seem to correspond to evolutionary breakpoints. These bands are likely to be involved in chromosome fragility or instability. In Primates, some biomarkers of genetic damage may be associated with various degrees of genomic instability. Here, we investigated the usefulness of Sister Chromatid Exchange as a biomarker of potential sites of frequent chromosome breakage and rearrangement in Alouatta caraya, Ateles chamek, Ateles paniscus, and Cebus cay. These Neotropical species have particular genomic and chromosomal features allowing the analysis of genomic instability for comparative purposes. We determined the frequency of spontaneous induction of Sister Chromatid Exchanges and assessed the relationship between these and structural rearrangements implicated in the evolution of the primates of interest. Overall, A. caraya and C. cay presented a low proportion of statistically significant unstable bands, suggesting fairly stable genomes and the existence of some kind of protection against endogenous damage. In contrast, Ateles showed a highly significant proportion of unstable bands; these were mainly found in the rearranged regions, which is consistent with the numerous genomic reorganizations that might have occurred during the evolution of this genus.