Packaging of bananas in containers having designed permeabilities to oxygen, carbon dioxide, and ethylene. The containers 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 bags in which they have been transported. In addition, bananas can be preserved in a satisfactory ripened state for longer periods of time.