Danish Princess Benedikte, in flowing green chiffon and glistening diamonds, represented Denmark's royal family last night at the opening of the Royal Danish Ballet and at an embassy party later. Her husband, Prince Richard-Casimir zu Sayn-Wittgenstein-Berleburg, couldn't make it. But her lady-in-waiting, Countess Trampe, was close by.

"Gosh, she really does look like a princess," said socialite Jan Shepard at a champagne reception before the Kennedy Center performance. "I just have to go meet her."

"She's a marvelous horsewoman, too," said Frida Burling. "She came to lunch at our Middleburg farm last fall and she wanted to see horses. Well, our horses aren't that great so I took her over to Paul Mellon's. You can't beat the horses there. And being of Danish ancestry, I just loved it. I said to my Danish grandmother up in the sky, 'Can you believe I have the princess here?' "

It seemed that no one could believe there was a real lady-in-waiting in the wings either. And no one was exactly sure what royal duties such a lady performs. But since such ladies are not often found at Kennedy Center openings, everyone marveled over the countess.

"I guess they just wait," said Daniel Boorstin, the librarian of Congress.

"They do any little thing, they just try to be helpful," piped up Ruth Boorstin. "They're companions. They're really equals."

"Oh no, they're not equals," interrupted another woman. "A princess is royalty."

The countess, who never moves out of the princess' view, has been with Benedikte for 14 years. "And my husband is a royal master for the Queen Mother Ingrid," she said.

"The queen, Margrethe Benedikte's sister , has three ladies-in-waiting. They must be with her every day," said the countess. "The princess lives in Germany and I am just her lady when she travels and when she is in Denmark," explained the countess. "There are just so many little things to do . . . "

The evening began last night with the champagne reception before the ballet in the Golden Circle Lounge, where Kennedy Center patrons each year pay dearly to meet princesses and other celebrities.

In the foyer outside the Kennedy Center Opera House, the princess opened an exhibition called "Far From Denmark," made up of ballet photographs by the Danish artist John R. Johnsen.

Following the show, guests and members of the ballet troupe were invited back to the Danish Embassy by Ambassador Otto Borch for a buffet supper of smoked salmon, roast beef and strawberries the size of plums.

"The performance was just marvelous," said Robert McNamara. "At first I thought it was like a German costume play. But it was much more than that. It was simply beautiful."

"It was just like a painting," said Joan Braden, who was escorted by McNamara. "All the colors were just beautiful."

Among the other guests were Chief of Protocol Selwa Roosevelt and her husband Archibald, William and Deeda Blair, Robert McNamara, S. Dillon Ripley, secretary of the Smithsonian, and Mary Ripley, Sen. Charles Percy (R-Ill.) and his wife Lorraine and National Endowment for the Arts Chairman Frank Hodsoll.

Members of the troupe filed in and headed straight for the princess. They bowed or curtsied. It was the troupe's first time in the United States in six years. "No, they don't travel very much," said the Royal Theatre's managing director, Henrik Bearing Liisberg. "Our taxpayers want to see them at home. After all, they are paying for it."