A closure for releasably securing to a container adapted for storing foodstuff or a beverage, the closure comprising closing means (14) for closing a mouth of the container and securing means (22,23) for securing it in a closed position, the closing means and the securing means being formed of a plastics material comprising polyoxymethylene so as to provide a substantial gas barrier to the passage of oxygen and/or carbon dioxide therethrough, The closure may have a sealing member (18) formed of resilient material (compared to the rigid material of the remainder of the closure) for providing a seal between the closure and the container. The sealing member may be provided on a bore component which projects into the container so that, in use, it seals against an internal surface of the container. The sealing member may be an o-ring (18) formed of an elastomer, e.g. nitrile butadiene rubber. A foodstuff or beverage container, e.g. in the shape of a wine glass or the shape of a beer glass, having such a closure is also described. The use of a plastics material comprising polyoxymethylene for closing a container provides a barrier to the ingress of oxygen and/or to the egress of carbon dioxide to improve the shelf life of the product is also described.