Nuts are susceptible to going rancid. It is better to store them in a cool and dry area. You should also refrigerate them on a sealed plastic or glass container. If you intend to keep them for a long period of time, you can freeze them. Nuts are also "re-freezable". After opening, keep the nuts in an airtight container.
Whole, shelled nutmeats remain fresh longer than nuts in pieces. It is better to Chop the Nuts just before you plan on using them.
Keep the Nuts away from onions and other high-odor foods (Nuts will readily take on the smell of things around them).