A taxonomic study of the 6 species of Stipa that inhabit desert regions of the Puna de Atacama S. Bomani Haum., S. venusta Phil., S. obtusa [Nees et Mey.] Hitchc., S. rigidiseta [Pilg.] Hitchc., S. saltensis O. Kuntze, and the new species S. Henrardiana) indicates that they constitute a natural group which I designate Obtusae, using as type the species S. obtusa which is the one with priority. The group is characterised by setose leaves, with ligules 3 to 10 mm long, by glumes that are scarious, smooth, depressed and usually unequal, by the fusiform anthoecium with the palea as long as the lemma and by glabrous anthers. These characters reveal a close relationship with Orthachne Nees and Oryzopsis Michx. More detailed studies are necessary to decide the generic relationships. Some of the species studied ( S. Bomani and S. saltensis) contain cyanoglucosides in their vegetative organs and consequently are feared by the inhabitants of the Puna as being toxic to livestock.