A new nomenclature of the lung lobes and of the bronchial tree is presented, with which the lungs in 40 species of 11 rodent families are described. Whole, fixed lungs and silicone casts of the bronchial tree are tested for 23 characters, based on the distribution of lung lobes, the number and geometry of first order bronchi, the pulmonary blood supply, and lung symmetry. Ten lung morphotypes are recognized, seven of them representing one or more families: Castor type (Castoridae), Cryptomys type (Bathyergidae), Ctenodactylus type (Ctenodactylidae), Eliomys type (Gliridae), Myocastor type (Myocastoridae), Octodon type (Octodontidae and Echimyidae) and Rattus type (Sciuridae, Muridae pt. and Dipodidae). The Hydromys type is found only in Hydromys chrysogaster (Muridae), while Galea type A and B both appear in Galea musteloides (Caviidae). The data are phylogenetically analyzed by the program PAUP 4.0 using as outgroup Lagomorpha or Insectivora. On the species level, there are no well-resolved cladograms. On the family level, the cladograms do not contradict traditional rodent systematics with one exception: the Caviidae do not fall within Caviomorpha or even within the Hystricomorpha, but form a sister group to Dipodidae (Myomorpha). This appears to be a result of convergence. The lungs of Gliridae are more similar to those of Muridae than to those of Sciuridae. Included in the ingroup, Oryctolagus (Lagomorpha) forms a clade with Caviidae + Dipodidae. Thus, the "Glires hypothesis" is neither supported nor refuted.