A closure made of metal or plastic for a container for accommodating beverages or food has a mouth opening which is to be closed by the container closure. The container closure has a sealing insert which is arranged such that it closes the mouth opening with sealing action when the container closure is fitted on the container. The container closure, including the sealing insert, does not contain any halogen-containing material, and the sealing insert comprises at least two different polymers, of which at least one is a barrier polymer with a Shore D hardness of at most 40 and oxygen permeability of at most 1000 cm3·100 μm/m2·d·bar and, without the Shore D hardness being limited, with oxygen permeability of at most 10 cm3·100 μm/m2·d·bar.