Alexandria's Birchmere may not be the only nightclub where people play bridge and Old Maid, and it may not be the only one where they read books and write letters, but it must be the only one where children do their homework while waiting for the show to begin.

That's because the Birchmere books only bluegrass acts -- "We're the only pure bluegrass club in the world," says owner Gary Oelze -- and bluegrass isn't just redneck or good-ol'-boy music, it's down-home music, God-how-I-miss-the-country music, gospel music, sing-along music, family music.

The club is in its second year in a converted store on Mount Vernon Avenue hard by the Arlington-Alexandria line, and almost every one of the 300 seats is filled almost every night it's open (Tuesday through Saturday). It's half-again as big as the Arlington quarters where it opened in 1974, and the acoustics are much better, but the Birchmere hasn't changed except to raise the cover charge to $5 weeknights and $6 on weekends, $8 when two groups play. The club's ambiance comes from the music and the patrons rather than the decor, which is best described as real plain.

Washington is the acknowledged capital city of bluegrass, and the Birchmere is the capital's capitol. Last weekend it offered a rare chance to hear both ends of the spectrum of mainstream bluegrass: the traditionalist Country Gentlemen on Friday and the progressive Seldom Scene on Saturday.Bill Monroe invented the bluegrass style; critics commonly say the Gentlemen made it popular and the Seldom Scene made it respectable. Whatever, they're both damn good, and they set the houses afire. Sooner or later every good 'grass group or solo artist shows up -- the sooner the better for the newcomers, because if you haven't played the Birchmere you don't count, hardly.

The club's clientele cannot be categorized. They range from babies to grandmothers and wear everything from non-counturier jeans to full-length mink. Cheek-by-jowl may be found carpenters humming and debutantes slumming; if they have anything in common besides love of the music, it's cheerful acceptance of whoever takes any vacant charis left at the table. When a group of teen-age girls takes a table alone, nobody bothers them, and wouldn't even if owner Oelze weren't keeping a cheerful but very sharp eye on things.

There are no reservations to be had at the Birchmere. The doors open at 7, and after that it's first-come, first-pick until the show begins (8:30 on weeknights, 9 on weekends). Which is why most of the cognoscenti bring their pocket electronic games or their sewing or whatever to pass the time; others just visit around.

"To tell the truth, I come for the early part," said Aileen Marant, a Canadian student who brought her little brother Bobby, visiting from Saskatchewan, Saturday night. "I live just about across the street, and I just come and read; I like being around these people, they remind me of home."

Those who arrive too late to capture one of the folding chairs generally can count on being seated after the first set (of, usually, three), because most of the families with school-age children leave then.

Those who come hungry may be sorry. "I always say that what we promise is great music, not great food," said Oelze, with precision. Everything is either pan-fried or deep-fried, and when the lights are low it may not be easy to tell whether you're eating French fries, your companion's fried clams or a neighbor's fried shrimp. Draft beer runs from $1.50 a glass to $7 a pitcher, soft drinks from 50 cents to $3.50 a pitcher. THE BIRCHMERE

3901 Mount Vernon Avenue, Alexandria (two blocks off South Glebe Road). Open Tuesday through Saturday from 7, first set at 8:30 weeknights, 9 weekends. No reservations; cover $5 to $8, 549-5919.