A membrane with at least one passage extending through an elastic material of the membrane, wherein when a cannula is inserted in the passage, the passage is expanded and the elastic material presses against the cannula and surrounds the cannula in a seal, wherein the membrane can be compressed relative to the passage, and wherein, in one embodiment, the passage exhibits a cross-sectional area having a long main axis and a short main axis perpendicular to the long main axis. The invention encompasses a membrane-cannula combination for biological and medical uses, and a membrane-connecting device combination for connecting a fluid guide and a catheter.