The appliance (20) connectable to a device (2) for the extracorporeal oxygenation of blood of the type comprising at least an inlet connection (3a) and an outlet connection (3b) for the blood, at least an inlet channel (4a) and an outlet channel (4b) for a work gas intended to supply oxygen to blood and/or remove CO2 from the same, comprises first sensor means (21) which can be positioned along at least one between the inlet and outlet connections (3a, 3b) of blood to read at least a characteristic blood value (Vb) corresponding to the blood pressure (PbinPbout) along one between said inlet connection (3a) and said outlet connection (3b) or to the blood pressure interval (Apb) between them, second sensor means (22) which can be positioned along at least one between the inlet and outlet channels (4a, 4b) of gas to read at least a characteristic gas value (Vg) corresponding to the gas pressure (pgin, pgout) along one between said inlet channel (4a) and said outlet channel (4b) or to the gas pressure interval (Apg) between them and variation means (23) for varying at least the gas pressure along the inlet channel (4a) and/or along the outlet channel (4b), wherein said variation means (23) are operatively connected to said first and second sensor means (21, 22) and are programmed to make the difference between said characteristic gas value (Vg) read by said second sensor means (22) and said characteristic blood value (Vb) read by said first sensor means (21) substantially equal to at least a predefined value.Linvention concerne un appareil (20) pouvant être relié à un dispositif (2) pour loxygénation extracorporelle du sang du type comprenant au moins une liaison dentrée (3a) et une liaison de sortie (3b) pour le sang, au moins un canal dentrée (4a) et un canal de sortie (4b) pour un gaz de travail destiné à fournir de loxygène au sang et/ou éliminer le CO2 de celui-ci, qui comprend un premier moyen de capteur (21) qui peut être positionné le long dau moins lune des lia