Robert Reilly believes that waltzing can stop war.

Last week he invited a few hundred of his friends and acquaintances to his annual peacekeeping party, a night of waltzing reminiscent of the sumptuous balls of turn-of-the-century Vienna.

The swish of satin and taffeta blended with lilting waltz music as men in white tie and tails whirled women in floor-length gowns around the palatial ballroom of the Organization of American States, the annual scene of Reilly's party.

It was a night of silk top hats, furs, dance cards, champagne and flaming crepes as more than 200 couples, including several high-ranking Reagan administration officials and young Republican professionals, most of whom are city residents, savored the third annual party of the Committee for Western Civilization.

"Between the Congress of Vienna and the outbreak of World War I, the world enjoyed an unequaled period of grace and tranquility," said Reilly, a Capitol Hill resident, White House staff member and party sponsor.

"Can it be only coincidence that it was precisely at that time that the waltz reached the apex of its popularity?"

He said the party had no political purpose, although the crowd was overwhelmingly Republican and the nearly $1,000 profit went to the Intercollegiate Studies Institute, founded by conservative author William Buckley Jr. in 1953 to sponsor seminars and publications for college students on such "traditional" values as capitalism.

The committee's board includes former national security affairs adviser Richard Allen, Sen. Phil Gramm (R-Tex.), former ambassador Clare Booth Luce, a half-dozen other former or current Reagan appointees and an Austrian baron.

"At the first dance in 1983 people kept waiting all night for an announcement, a pitch, but it's just fun," Reilly said.

Reilly, resplendent in top hat, white tails, flowing cape and gloves, cut a striking figure on the dance floor as he waltzed most numbers.

By midevening, beads of perspiration dripped on his formal attire despite his repeated wipings with one of his white gloves.

Tables swathed in white linen cloths and topped with single candlesticks and spring flowers ringed the dance floor.

Nearby were long tables, lit by silver candelabras and laden with rich desserts, fruits and cheese.

Champagne and other drinks were plentiful at an open bar next to the dance floor.

"I love it. I wouldn't miss this for the world," said Jane Shepard, a native of Washington and a Capitol Hill resident who wore a black net gown that was embossed with a maze of gold polka dots and diamonds and cinched with a shiny gold belt.

"It reminds me of when I was growing up and you had to go to cotillions all the time," she said.

Michelle Van Cleave, also a Capitol Hill resident and legislative assistant to Rep. Jack Kemp (R-N.Y.), said, "Frequently when you go do dances most people spend the night on the sidelines drinking, talking and eating, and dancing is a sidelight.

At this particular party, dancing is the object, and everyone is dancing enthusiastically."

"It is an exceptionally elegant evening because of good friends, lovely music and the waltz," she added.

The plethora of designer gowns, tuxedos and furs echoed the inaugural parties of last month. Some of the women confessed to recycling their inuaugural finery for the waltz.

Elayne Bennett, wife of the new secretary of education, said her turquoise silk shantung sheath by Halston came from a sale rack and had been her inaugural gown.

Other gowns came from designers Christian Dior, Mollie Parnis and Adolpho. Faith Whittlesey, White House public liaison chief rumored to be headed for another stint as Swiss ambassador, wore a bright orange Greek print with gold trim that she said was selected from her collection of evening gowns acquired during her diplomatic days.

"It's very festive; that's why I decided to wear it," she said.

The guests included such notables as OAS Ambassador William Middendorf and Secretary of Education William Bennett, a handful of barons, dukes and countesses, and Reagan supporters ranging from White House and presidential commission staff members to employes of the American Enterprise Institute and the Heritage Foundation, conservative think tanks.

"It is a good thing that something like this still occurs in our time of equalization," said Gottfried Dietze, 62, of Foggy Bottom, a political science professor, as he danced the last waltz of the evening, the Blue Danube. "This is class."