Packaging of bananas in containers, for example polyethylene bags, having designed permeabilities to oxygen, carbon dioxide, and ethylene. The bags preferably include a gas-permeable membrane comprising (1) a microporous film, and (2) a polymeric coating on the microporous film. The containers enable storage and/or ripening of bananas under controlled conditions. Using the new containers, bananas can be ripened while they are being transported, or in conventional ripening rooms without opening the containers in which they have been transported, or after they have left a ripening room. In addition, bananas can be preserved in a satisfactory ripened state for longer periods of time.