There are many types of pests that are attracted to paper. Contact your local agricultural extension service or an entomologist for accurate identification. Chemical treatment (fumigation) may permanently damage record materials and should be avoided. Instead, attempt to address the source of the infestation: seal all possible entry points; promptly remove or seal up pest lures, such as food or trash; keep temperature and relative humidity low; and keep the area clean and dust-free.
If the infestation affects only part of your collection, isolate the materials in a tightly sealed plastic bag and consult a preservation professional. Pests found in records are most commonly the types attracted to damp conditions. If the infestation is wide-spread, it is likely there is excess moisture present that must be located and the resulting high relative humidity eliminated. Spread the records out in a cool, dry location with plenty of air circulation. This should drive the pests away. As long as proper conditions are maintained, any eggs left behind will not hatch and offspring will either not survive or move on to a more hospitable environment.