We examined the structure-function relationships that underlie the aerobic capacities of marsupial mammals that hop. Marsupials have relatively low basal metabolic rates (BMR) and historically were seen as 'low energy' mammals. However, the red kangaroo, Macropus rufus, (Family Macropodidae) has aerobic capacities equivalent to athletic placentals. It has an extreme aerobic scope (fAS) and its large locomotor muscles feature high mitochondrial and capillary volumes. M. rufus belongs to a modern group of kangaroos and its great fAS is not general for marsupials. However, other hopping marsupials may have elevated aerobic capacities. Bettongia penicillata, a rat-kangaroo (Family Potoroidae), is a small (1 kg) active hopper whose fAS is somewhat elevated. We examined the oxygen delivery system in its muscles to ascertain links with hopping. An elevated fAS of 23 provided a relatively high VO2max in B. penicillata; associated with this is a skeletal muscle mass of 44% of body mass. Ten muscles were sampled to estimate the total mitochondrial and capillary volume of the locomotor muscles. Values in B. penicillata were similar to those in M. rufus and in athletic placentals. This small hopper had high muscle mitochondrial volume densities (7.1-11.9%), and both a large total capillary volume (6 ml kg-1 body mass) and total capillary erythrocyte volume (3.2 ml kg-1). Apparently, a considerable aerobic capacity is required to achieve the benefits of the extended stride in fast hopping. Of note, the ratio of VO2max to total muscle mitochondrial volume in B. penicillata was 4.9 ml O2 min-1 ml-1. Similar values occur in M. rufus and also placental mammals generally, not only athletic species. If such relationships occur in other marsupials, a fundamental structure-function relationship for oxygen delivery to muscles likely originated with or before the earliest mammals.