The invention provides an ostomy bag assembly comprising outer (2) and inner (4) bags secured to one side of a flange wherein:the flange (6) comprises a polymeric backing film (8) and a layer of bioadhesive (10) for securing the ostomy bag assembly to the body of a patientthe outer bag is detachably bonded to a first attachment zone (14) on the polymeric backing film of the flange by means of an annular bonding element (22) which is interposed between the outer bag and the first attachment zonethe inner bag is secured to a second attachment zone on the polymeric backing film of the flangethe annular bonding element is formed from a multilayer polymeric material comprising first and second ethylene vinyl acetate layers and a polymeric support layer interposed therebetween andthe first ethylene vinyl acetate layer has a coating of an ethylene vinyl acetate copolymer adhesive thereon.