SUMMARYAvian cranial kinesis, in which mobility of the quadrate, pterygoid and palatine bones contribute to upper bill elevation, is believed to occur in all extant birds. The most widely accepted model for upper bill elevation is that the quadrate rotates rostrally and medially towards the pterygoid, transferring force to the mobile pterygoid-palatine complex, which pushes on the upper bill. Until now, however, it has not been possible to test this hypothesis in vivo because quadrate motions are rapid, three-dimensionally complex and not visible externally. Here we use a new in vivo X-ray motion analysis technique, X-ray reconstruction of moving morphology (XROMM), to create precise (±0.06mm) 3-D animations of the quadrate, braincase, upper bill and mandible of three mallard ducks, Anas platyrhynchos. We defined a joint coordinate system (JCS) for the quadrato-squamosal joint with the axes aligned to the anatomical planes of the skull. In this coordinate system, the quadrate's 3-D rotations produce an elliptical path of pterygoid process motion, with medial and rostrodorsal then lateral and rostrodorsal motion as the upper bill elevates. As the upper bill depresses, the pterygoid process continues along the ellipsoidal path, with lateral and caudoventral then medial and caudoventral motion. We also found that the mandibular rami bow outwards (streptognathy) during mandibular depression, which may cause the lateral component of quadrate rotation that we observed. Relative to the JCS aligned with the anatomical planes of the skull, a second JCS aligned with quadrato-squamosal joint anatomy did not produce a simpler description of quadrate kinematics. Supplementary material available online at