Abstract: A container for a liquid radioactive and/or fissionable substance includes an outer container. An inner container is disposed in said outer container for receiving the substance. The inner container includes a primary container and a separate, closed secondary container having upper and lower ends. The primary container has an upper end protruding beyond said upper end of said secondary container and a lower end protruding beyond said lower end of said secondary container in longitudinal direction. A first connecting tube leads continuously downward in a direction from said lower end of said secondary container toward said lower end of said primary container. A second connecting tube leads continuously upward from said upper end of said secondary container in a direction toward said upper end of said primary container. The outer container has a fill chamber disposed therein for filling with heat-conducting filler.