Cooked mussels will keep best in a sealed container. Select a container with a lid that closes tightly, or put your cooked mussels in a zipper-top bag. If you wish, you can place the cooking broth in the container with the mussels. Once cooked, your mussels should stay fresh in the refrigerator for 1-4 days. Throw away any mussels that are left over after 4 days have passed. Before eating any cooked mussels, check for an unpleasant odor or a slimy texture. These are signs that the mussel has gone bad, and should not be eaten. Avoid contaminating your cooked mussels with bacteria and dirt by storing them away from uncooked mussels and other shellfish. Always wash your hands and utensils with warm water and soap after handling uncooked shellfish.

Summary:
Place the cooked mussels in a container. Store your mussels in the refrigerator for no more than 4 days. Keep the cooked mussels separate from any uncooked shellfish.