A connection device for connecting a headgear (11) and a mask (10) and a system for supplying a flow of gas to a patient that incorporates such a connection device. The connection device allows independent rotation of each of two independently disconnecting headgear connectors. The gas delivery mask includes a shell (14, 14, 14, 62), a first connector (28, 28, 28, 60) associated with the shell, a second connector (42, 42, 74) connected to a headgear and realeasably and rotateably connected to the first connector.Linvention concerne un dispositif de raccordement, permettant de raccorder un casque (11) et un masque (10), ainsi quun système permettant le transfert dun flux de gaz vers un patient et incorporant ledit dispositif de raccordement. Ce dispositif de raccordement permet une rotation indépendante de deux raccords de casque à démontage indépendant. Ce masque à gaz comporte une coquille (14, 14, 14, 62), un premier raccord (28, 28, 28, 60), associé à ladite coquille, et un second raccord (42, 42, 74) relié à un casque et relié au premier raccord de façon amovible et rotative.