Abstract: A double container system for transporting and storing radioactive waste erials includes an inner storage container of steel for enclosing the radioactive material to be stored in a gas-tight manner and an outer shielding container which provides for the necessary shielding effect and mechanical security with regard to handling and transportation. A neutron moderator layer is disposed in an annular gap between the outer shielding container and the inner storage container. The neutron moderate layer is made of hydrogen-bearing material, preferably polyethylene. In order to provide a good shielding effect while at the same time providing very good conduction of heat from the inside to the outside, the moderator layer includes individual rings of polyethylene which are stacked one above the other. Arranged between each two mutually adjacent ones of the polyethylene rings is a ring of a heat-conducting metal material having an H-profile when viewed in radial section.