Apparatus for separating the gaseous hydrogen isotopes protium, deuterium and tritium from a gas stream containing one or a plurality of the hydrogen isotopes. A membrane is provided which is permeable to the hydrogen isotopes and impermeable to the gas stream. The membrane has a side facing away from the gas stream and a side exposed to the gas stream. On the side of the membrane facing away from the gas stream, there is disposed a getter which takes up the hydrogen isotopes by absorption at a predetermined absorption temperature and releases the absorbed hydrogen isotopes again by desorption at a desorption temperature above the absorption temperature. The membrane permeable to the hydrogen isotopes covers a surface of the getter so that the getter, at the absorption temperature, absorbs hydrogen isotopes exclusively through the membrane. The membrane and getter constitute an absorption element and are permanently connected to one another.