Tasmanian devils (Sarcophilus harrisii) are evolving in response to a unique transmissible cancer, devil facial tumour disease (DFTD), first described in 1996. Persistence of wild populations and the recent emergence of a second independently evolved transmissible cancer suggest that transmissible cancers may be a recurrent feature in devils. Here, we compared signatures of selection across temporal scales to determine whether genes or gene pathways under contemporary selection (six to eight generations) have also been subject to historical selection (65-85 Myr). First, we used targeted sequencing, RAD-capture, in approximately 2500 devils in six populations to identify genomic regions subject to rapid evolution. We documented genome-wide contemporary evolution, including 186 candidate genes related to cell cycling and immune response. Then we used a molecular evolution approach to identify historical positive selection in devils compared to other marsupials and found evidence of selection in 1773 genes. However, we found limited overlap across time scales, with only 16 shared candidate genes, and no overlap in enriched functional gene sets. Our results are consistent with a novel, multi-locus evolutionary response of devils to DFTD. Our results can inform conservation by identifying high priority targets for genetic monitoring and guiding maintenance of adaptive potential in managed populations.