G- and C-banded chromosomes of Aethomys namaquensis (2n = 24), A. chrysophilus (2n = 44), and Praomys coucha (2n = 36) are compared and contrasted with published material on Australian Muridae and North American Sigmodontidae. Direction and types of chromosomal rearrangements are established using cladistic methodology. An acrocentric morphology for chromosomes 5, 14, 15 and 20 (numbering system from Peromyscus) are proposed as primitive for the common ancestor of the Muridae and Sigmodontidae rodent lineages. Reduced diploid number of Aethomys namaquensis is derived by eight tandem and five centric fusions since divergence from the common ancestor with A. chrysophilus. The two species of Aethomys share one derived metacentric chromosome that distinguishes them from Praomys. Praomys has unique chromosomes which can be derived from the proposed primitive condition by five centric fusions and five pericentric inversions. It is concluded that karyotypic orthoselection for tandem and centric fusions is best explained by cellular or biochemical mechanisms rather than variation in population characteristics.