Abstract. -The structure and function of the nasal conchae of extant reptiles, birds, and mammals are reviewed, and the relationships to endothermy of the mammalian elements are examined. Reptilian conchae are relatively simple, recurved structures, which bear primarily sensory (olfactory) epithelium. Conversely, the conchae, or turbinates, of birds and mammals are considerably more extensive and complex, and bear, in addition, nonsensory (respiratory) epithelium. Of the mammalian turbinates, only the exclusively respiratory maxilloturbinal has a clear functional relationship with endothermy, as it reduces desiccation associated with rapid and continuous pulmonary ventilation. The other mammalian turbinates principally retain the primitive, olfactory function of the nasal conchae. The maxilloturbinates are the first reliable morphological indicator of endothermy that can be used in the fossil record. In fossil mammals and mammallike reptiles, the presence and function ofturbinates are most readily revealed by the ridges by which they attach to the walls of the nasal cavity. Ridges for olfactory turbinals are located posterodorsally, away from the main flow ofrespiratory air, whereas those ofthe respiratory maxilloturbinals are situated in the anterolateral portion of the nasal passage, directly in the path of respired air. The maxilloturbinal is also characterized by its proximity to the opening ofthe nasolacrimal canal. Posterodorsal ridges, for olfactory turbinals, have long been recognized in many mammallike reptiles, including early forms such as pelycosaurs. However, ridges for respiratory turbinals have not been identified previously in this group. In this paper, the presence of anterolateral ridges, which most likely supported respiratory turbinals, is reported in the primitive therocephalian Glanosuchus and in several cynodonts. The presence of respiratory turbinals in these advanced mammallike reptiles suggests that the evolution of "mammalian" oxygen consumption rates may have begun as early as the Late Permian and developed in parallel in therocephalians and cynodonts. Full mammalian endothermy may have taken as much as 40 to 50 million yr to develop.