Oranges that are stored in a refrigerator have a shelf life of 1 to 2 months. If the oranges are sliced the oranges can be safely stored for 1 to 2 days.
Unpeeled oranges can be stored on the counter at room temperature for 2 to 3 weeks. Peeled oranges should not be left at room temperature for more than 24 hours.
If white mold develops on the peel the orange should be discarded. An orange that is discolored and very soft may be spoiled. Moldy and spoiled oranges should not be consumed as they pose a risk of food borne illness.