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Margie is a trusted home cook immersed in German foodways.
As long as the can is not damaged or bulging, the anchovies should be OK. Salt is a preservative and salted foods keep for a very long time.
June is a trusted source on General Cooking.
Unopened? They should last forever. Once opened, they will keep until you've used them up. Could take a while. Those are large cans!
pierino is a trusted source on General Cooking and Tough Love.
Per June's advice they will probably last longer than you will. However once the can is opened you should cover the top surface with more coarse salt and then refrigerate. Maybe cut out a circle of parchment or foil that fits the can and press that down on top.
Nancy is a food writer, historian, and author of many books, her most recent being Virgin Territory: Exploring the World of Olive Oil, forthcoming from Houghton Mifflin.
But keep the can well covered in your refrigerator. Anchovies are delicious but you don't necessarily want their flavor to invade your butter or other sensitive ingredients in the fridge.
Also, check the tin to see if there isn't a "use by" date somewhere on it. There should be, although those dates are sometimes in obscure places. Anchovies should last forever, but in real life nothing ever does!