Dances like Hunt the Squirrel, Patronella, The Dashing White Sergeant and The Physical Snob are hundreds of years old, but still alive in Washington.

Every weekend - on Friday and Sunday nights - District residents with a taste for traditional American and English country dancing get together for some fancy stepping at Concordia Church and Catholic University.

Most of the music for the allemandes, swings and do-si-doing is provided by fiddler Steve Hickman and his wife Linda on the flute, bass fiddle or tin whistle. They are backed up by their two dance bands, the Boss-Town Buzz Steps and the Violet Hills Swamp Donkeys. (The buzz step is a kind of country dance swing.)

This is not your romp-and-stompin' Western square dancing. The caller does not harangue the dancers or defy oxygen deficiency with constant patter. Instead, the tunes are traditional. The dances aresimple so that the movice, with some instruction, can join in. The calling is limited to brief directions, called prompts, and it's the music that inspires the dancers to step lively.

Hickman, an Alexandria resident, started dancing about the same time he started fiddling. It was 1969 and he was 21 years old, working in a District brokerage house and hating it.

That summer, he went to the Smithsonian Folk Life Festival and saw Walt Koken play the fiddle.

"What impressed me was that he played real old-time music - not 'Foggy Mountain Breakdown' and 'Orange Blossom Special,' but gobs of stuff I'd never heard before - and it really appealed to me."

So Hickman went out and bought himself a fiddle.

Shortly after that, the Hickmans went to a potluck supper at a friend's house in Accokeek, Md., where there was country dancing. Soon, they were dancing every weekend.

"After doing a dance eight or nine times, I'd be able to play the tune," said Hickman, who took violin lessons only a few months before he began to rely on his ear. "I guess the tunes you learn by ear are the ones your brain is the most pleased with."

He performed for a while with an old-time string band. Later, he and Linda started street playing in Georgetown. With their friends John Carter on guitar and Dennis Botzer on banjo, they called themselves the Violet Hills Swamp Donkeys.

In 1974, the music and dancing came together. Louis Shapiro, a mathematics professor at Federal City College, asked the Swamp Donkeys to play for a handful of people who met every Friday night for country dancing.

The group, called the D.C. Country Dancers, still meets Fridays at Concordia United Church of Christ at 1920 G St. NW. Now more than 100 dancers usually show up.Anyone is welcome, including beginners. Admission is $1.50, with proceeds going to the band.

For several years the calling was done by Bob Dalsemer, a prominent caller with a wide repertoire of Southern mountain square dances, collected from travels in the Appalachian Mountains. Now Hickman and other members of the band sometimes do the calling.

On Sundays, Hickman plays for another group of the Folklore Society of Greater Washington.

Here too, anyone is welcome who is willing to pay the $2 admission fee and try to keep up. The dances featured are New England and English quadrilles (squares) and contras (done in long lines of facing couples.).

The Sunday night hornpipes, jigs and reels from the British Isles - some dating back to the 17th and 18th centuries - required a band with a different sound. So Linda Hickman put down the bass fiddle and took up her flute, on which she had classical taining. Botzer switched from banjo to piano. Completing the group, called the Boss-Town Buzz Steps, are Laurie Andref, who plays accordion and Piano; David Shorey, a recorder player who works during the day as curator of musical instruments at the Library of Conress, and Richard Shuman, who plays mandolin and guitar.

As for the dancers, some swing and balance with style; others, with enthusiasm. The same people come back again and again - a waitress at Mr. Henry's, a drama major at Catholic University, a mid-level bureaucrat from the Occupational Safety and Health Administration.

By playing at bars, weddings and for other dancing groups, the Hickmans can devote themselves to music fulltime. Steve Hickman, 1976 winner of the National Scottish Open Fiddling Championship, has been teaching fiddle for two years at Glen Echo Park. He also is on the staff of Pinewoods, a summer dance camp near Buzzards Bay, Mass., run by the Country Dance and Song Society.

Whenever the occasion demands, Hickman comes up with a new band with a new name. He has organized the Scottish Findhorn Celidh Band, which dons kilts to play for a Scottish dance society; the Morning Star Ceili Band, which plays once a month for a group of Irish dancers, and Celtic Thunder, which plays at a Capitol Hill bar, The Dubliner.

Hickman plays bars because he needs the money, not because he likes that attention.

"Being on stage makes me nervous," he says. "I feel like you have to put on airs. There's the tension of portraying a good image all the time. And there's a sea of people out there looking at you that you never get to know, that it's hard to get a fix on.

"But playing for dance, the same people keep coming back," said Hickman, gesturing at the dancers at Catholic University. "Most of their faces I know real well, and I feel like I'm friends with them."