A controlled evacuation ostomy appliance comprises a membrane that is urged into sealing engagement with a stoma, by the generation of radial tension in the membrane. A tensioning device applies tension, with respect to the stoma, at one or more positions that are (i) outboard of the periphery of the projecting portion of the stoma, and/or (ii) between the level of the peristomal skin and the level of the most projecting part of the stoma. Tension limiting means are disclosed. The membrane may be gas-permeable to allow flatus to be vented.
