The current hypothesis regarding the mechanics of breathing in crocodylians is that the double-headed ribs, with both a capitulum and tuberculum, rotate about a constrained axis passing through the two articulations; moreover, this axis shifts in the caudal thoracic ribs, as the vertebral parapophysis moves from the centrum to the transverse process. Additionally, the ventral ribcage in crocodylians is thought to possess additional degrees of freedom through mobile intermediate ribs. In this study, X-ray reconstruction of moving morphology (XROMM) was used to quantify rib rotation during breathing in American alligators. Whilst costovertebral joint anatomy predicted overall patterns of motion across the ribcage (decreased bucket handle motion and increased calliper motion), there were significant deviations: anatomical axes overestimated pump handle motion and, generally, ribs in vivo rotate about all three body axes more equally than predicted. The intermediate ribs are mobile, with a high degree of rotation measured about the dorsal intracostal joints, especially in the more caudal ribs. Motion of the sternal ribs became increasingly complex caudally, owing to a combination of the movements of the vertebral and intermediate segments. As the crocodylian ribcage is sometimes used as a model for the ancestral archosaur, these results have important implications for how rib motion is reconstructed in fossil taxa, and illustrate the difficulties in reconstructing rib movement based on osteology alone.