IF YOU'VE RUN short of things to worry about more than six million books at the Library of Congress are in such bad shape that they would be fatally damaged if used. Back in 1970, the Library called in an English expert, Peter Waters, to head the Office of Restoration. He launched on-the-job training of book and paper conservators, laid down a rigorous curriculum of chemistry, history and work-bench practice and set out to find the first of 17 apprentices (civil servants with GS ratings) in the only program of its kind in the country.

"We looked for manual desterity, inquiring minds an interest in craft," he says. To his surprise - bookbinders in England are mostly male - he turned up more qualified women than men. There are no vacancies in the program at the present time, and it has had only one drop-out since it began.

Only a book labeled "rare" (meaning an artifact of intrinsic value) is sent to the restoration workrooms to be saved.Peters Waters and his helpers then take a history, make lab tests and decide on the medicine. "We never sacrifice a manuscript to the treatment ," he says. "If repairing a rare book will substantially change it, we leave it alone." (Books get a third of their time - rare manuscripts and "works of art on parper" the rest)

It takes at least seven years in class and on the bench to make a master binder-conservator.Thomas Albro has been at it for five and a half, and already teaches bookbinding - including simple restoration techniques - in the Smithsonian Resident Associate program. Like some of his collegues, he has a private practice on the side and his own workshop at home in Arlington. (House calls in emergencies only.)

Other help for ailing books is at hand: Library of Congress Preservation Leaflets tell what to do for leather binding when red rot sets in and how to fend off acidity - which causes today's books to turn yellow and self-destruct. (Write Assistant Director of Preservation, Library of Congress. Washington, D.C. 20540.)

Meanwhile, Peter Waters suggests home remedies: never store a valued book in the attic (too hot) or in the basement (might flood) or in direct sunlight (will fade). And never, never patch a damaged treasure with transparent cellophane tape. . . . And Book Sleuths

IS A VOLUME of your Britannica gone? Or somebody snitched your Saki? Do not despair. Operating out of basements, the back rooms of book stores and in their own homes, a small but dogged band of Washington book-researchers will track down missing links in your library, no questions asked - except: Are you sure it's out of print? (Current books you have to find on your own.) And have you got the title straight? ("That big coffee-table book about Renoir" is not quite enough - but they'll sometimes give it a try.)

Among the Olympic-caliber search teams are Joan and Reading Black, who have operated Book Search (451-4055) out of their house in Springfield, Virginia for the last eight years. "We're not a book store," Mrs. Black says. "We're exclusively a search service by mail and phone." Their clients range from big institutions to individuals. Every two weeks they send a bulletin to 326 book dealers and scouts all over this country and in English-speaking countries abroad - eight legal-sized pages, single-spaced, listing the books they're currently searching for. They also run in the Antiquarian Bookman (known as "The AB" among book searchers), a weekly listing of wanted books that costs $55 a year. The Blacks charge a minimum of $7 for a book (if you decide you want it), and they've been searching for some books for eight years. Every four months they ask their clients if they're still interested.

John Desch has been running down books for people since he retired from the Bureau of Public Roads and opened the OP (for Out of Print) Bookshop in Wheaton 15 years ago. He has 25,000 out-of-print paperbacks plus 25,000 out-of-print hardbacks as working capital to search through. He specializes in "Americana" - but says he'll try anything (946-9609).

Philip Burgess of Second Story Books has a basement command-post under the store on Connecticut Avenue, with a green plastic Neat 'N Tidy bucket hanging from the radiator, a radio going, a hotline telephone on his desk and what his boss calls the world's largest card file. Burgress came to book-searching out of computer software and telephone marketing, and has clients from as far away as Algiers (244-5550).

Aladdin's International Book Store (on Rockville Pike, behind Memco), owned by All-Obaidy, an urban development consultant from Dhahran and his wife, who teaches English, searches only for foreign books for clients all over the world. On his urban consulting trips abroad, All-Obaidy scouts for books on the side (468-0098).

Quill and Brush in Bethesda reports that a third of its business is looking for books. "Since we're a collectors' book shop, we 've had success in finding unusual items," says Pat Ahearn, the owner (652-5848). In addition to it monthly Sunday auctions, Economy Books in Alexandria searches for books for its clients (549-9330). Yesterday's Books on Wisconsin Avenue advertises in "The AB" for its clients, "if they really want a book" (363-0581). And although Bookhouse in Arlington and Booked Up in Georgetown don't search for books, they watch for books they know their clients want.

Current sought-after titles? Old cookbooks and The Alexandria Quartet.