Abstract: A two-piece ostomy appliance in which one of the components, preferably the pouch component, is provided with a dual-state, bistable coupling ring for sealingly engaging the companion ring of the other (e.g., faceplate) component. The ring is formed of relatively stiff but flexible plastic material and is capable of assuming two stable states or conditions. In one such state, its normal one, the ring is substantially untensioned and its configuration is frusto-conical; in its other state, the direction of the conical taper is reversed or inverted and the ring again assumes a stable but now tensioned condition. When in its normal state, the ring has an inside diameter substantially smaller than in its inverted state, so that in mating such rings together, a user may enlarge the opening to facilitate joining the parts together and may then return the bistable ring to its normal state to insure a secure, fluid-tight seal between the parts.