Bats (order Chiroptera) are the longest lived mammals for their size, with particularly extreme longevity evolving in the family Vespertilionidae, or vesper bats. Because of this, researchers have proposed using bats to study ageing and cancer suppression. Here, we study gene duplications across mammalian genomes and show that, similar to previous findings in elephants, bats have experienced duplications of the tumor suppressor gene TP53, including five genomic copies in the genome of the little brown bat (Myotis lucifugus) and two copies in Brandt's bat (Myotis brandtii). These species can live 37 and 41 years, respectively, despite having an adult body mass of only ~7 grams. We use evolutionary genetics and next generation sequencing approaches to show that positive selection has acted on the TP53 locus across bats, and two recently duplicated TP53 gene copies in the little brown bat are both highly conserved and expressed, suggesting they are functional. We also report an extraordinary genomic copy number expansion of the tumor suppressor gene FBXO31 in the common ancestor of vesper bats which accelerated in the Myotis lineage, leading to 34\u201457 copies and the expression of 20 functional FBXO31 homologs in Brandt's bat. As FBXO31 directs the degradation of MDM2, which is a negative regulator of TP53, we suggest that increased expression of both FBXO31 and TP53 may be related to an enhanced DNA-damage response to genotoxic stress brought on by long lifespans and rapid metabolic rates in bats.