Leeks are so hardy they are usually stored in the ground and harvested as needed (cover with mulch in cold climates). The outer skin may turn somewhat slimy in very cold weather, but the interior should be fine.

Storage Req: Ground
Storage Temp: °F
Storage Length: days

You can store leeks for several weeks in a plastic bag in the fridge.

Storage Req: Refrigerator
Storage Temp: 35-40°F
Storage Length: 1-21 days

In very cold climates you can store Leeks in a root cellar at 32 to 40˚ F. Trim off the excess tops and roots and plant them in a box of damp sand.

Storage Req: Cold, Moist
Storage Temp: 32-40°F
Storage Length: 1-60 days