Recent didelphid marsupials resemble the assumed mammalian ancestor and are suitable to inform on the evolution of the mammalian lung. This study uses X-ray computed tomography (μCT) to three-dimensionally reconstruct the bronchial tree of the marsupial Gray short-tailed opossum (Monodelphis domestica) in order to reveal the timeline of morphogenesis during the postnatal period. The development of the bronchial tree was examined in 37 animals from embryonic day 13, during the postnatal period (neonate to 57 days) and in adults. The first appearance and the branching of lobar, segmental and sub-segmental bronchioles in the lungs were documented. Based on the reconstructions, the generation of end-branching airways, the median and maximum generation and the number of branches were calculated for each pulmonary lobe. At birth, the lung of M. domestica has a primitive appearance since it consists of a simple system of branching airways that end in a number of terminal air spaces, lobar bronchioles, and first segmental bronchioles are present. During the postnatal period, the volumes of the lung and bronchial tree steadily increase and development, differentiation, and expansion of the bronchial tree takes place. By 14 days, the fundamental bronchial tree consisting of lobar, segmental, and sub-segmental bronchioles has been established. A mature bronchial tree, including respiratory bronchioles and alveolar ducts is present by day 35. The asymmetry of the right (predominately four lobes) and the left lung (predominately two lobes), as present in M. domestica, can be considered as plesiomorphic for Mammalia. In marsupials, the process of branching morphogenesis, which takes place intrauterine in the placental fetus, is shifted to the postnatal period, but follows similar patterns as described in placentals. Lung maturation in general and the branching morphogenesis in particular seems to be highly conservative within mammalian evolution.