Climate oscillations during the Quaternary altered the distributions of terrestrial animals at a global scale. In mountainous regions, temperature fluctuations may have led to shifts in range size and population size as species tracked their shifting habitats upslope or downslope. This creates the potential for both allopatric speciation and population size fluctuations, as species are either constrained to smaller patches of habitat at higher elevations or able to expand into broader areas at higher latitudes. We considered the impact of climate oscillations on three pairs of marsupial species from the Andes (Thylamys opossums) by inferring divergence times and demographic changes. We compare four different divergence dating approaches, using anywhere from one to 26 loci. Each pair comprises a northern (tropical) lineage and a southern (subtropical to temperate) lineage. We predicted that divergences would have occurred during the last interglacial (LIG) period approximately 125 000 years ago and that population sizes for northern and southern lineages would either contract or expand, respectively. Our results suggest that all three north–south pairs diverged in the late Pleistocene during or slightly after the LIG. The three northern lineages showed no signs of population expansion, whereas two southern lineages exhibited dramatic, recent expansions. We attribute the difference in responses between tropical and subtropical lineages to the availability of ‘montane-like’ habitats at lower elevations in regions at higher latitudes. We conclude that climate oscillations of the late Quaternary had a powerful impact on the evolutionary history of some of these species, both promoting speciation and leading to significant population size shifts.