Nancy Reagan and Raisa Gorbachev yesterday denied reports that they don't get along -- not in a joint communique' exactly, but nevertheless in a joint appearance during a 45-minute tour of the White House.

Mrs. Reagan may have thought she had dealt with the question once and for all when she talked to reporters while awaiting the arrival of her Soviet guest. The whole idea of competition between them, she said, was "so silly. It's so silly."

But in the East Room, where the two wound up the tour, the question popped up again. This time it was aimed at Mrs. Gorbachev. Mrs. Reagan looked aghast. Mrs. Gorbachev merely looked at Mrs. Reagan.

"I've answered that five times," snapped Mrs. Reagan.

"Everything is all right," noted Mrs. Gorbachev, her face betraying none of the emotion Mrs. Reagan seemed to feel. "And Mrs. Reagan gave the answer. She is the hostess and that was her word."

Nevertheless, the contrasting public personas of the two women were very much in evidence yesterday as Mrs. Gorbachev twice resisted Mrs. Reagan's attempts to steer her away from the press. Making it apparent that she wanted to chat longer, Mrs. Gorbachev at one point pulled her hand away from Mrs. Reagan's and turned to answer questions.

The White House tour was the result of a request Mrs. Gorbachev had made several weeks ago. Mrs. Reagan subsequently invited her to tea, but Mrs. Gorbachev didn't RSVPfor two weeks -- reportedly annoying Mrs. Reagan, who was trying to nail down her summit week schedule -- and then she informed her hostess that instead of an afternoon tea it would have to be a morning coffee. Later, it was learned that the problem was that both Gorbachevs had scheduled a teatime meeting with U.S. publishers.

But yesterday, none of that was brought up, and the tour got off to a cordial enough start with Mrs. Reagan in the role of guide and Mrs. Gorbachev the willing and curious tourist.

Mrs. Gorbachev's day had begun at the National Gallery of Art, where, quoting columnist Art Buchwald's dictum that the American tourist allots 6 1/2 minutes to see the Louvre, she whipped through in a bit over an hour. After the White House tour and coffee, she went on to Secretary of State George Shultz's lunch honoring her and her husband, and later in the day had the date with the publishers, topped off by the reciprocal dinner for the Reagans at the Soviet Embassy.

All along the way she appeared willing -- even eager -- to talk, to the press and everyone else.

At the top of the National Gallery's East Building staircase, she found time to talk to the gallery staff, which surprised her and NGA Director J. Carter Brown by turning up to applaud. She stopped as well at each of the five points on the tour where reporters were allowed to stand.

In the receiving line at the State Department lunch, she seemed so curious about the people she was meeting that handshakes turned into hand holding. She didn't let go until Helena Shultz, assisted by protocol officers, urged guests to move along.

She had obviously done her homework, too. But there were gaps. For instance, when she and Mrs. Reagan reached the State Dining Room (somehow, it seemed "smaller" than at the state dinner in the Gorbachevs' honor the night before, she said) she asked her hostess when the White House was built. The first lady, prepared with information on Lincoln's portrait hanging over the mantel, needed help on that one. Coming to the rescue was assistant curator Betty Monkman, who said the house was built "between 1782 and 1800."

There were other questions: Was the chandelier 19th-century? Was the painter of Abraham Lincoln's portrait well known? Was John Adams the first to move in? Did Jefferson live there?

"Here," said Mrs. Reagan, getting back to her role in the tour. "I want to show you something I really like." And she read the mantel's carved inscription written by Adams on his second night in the mansion, ending with his wish that "none but honest and wise men ever rule under this roof."

Mrs. Gorbachev nodded her head in agreement. "Indeed, only the honest and wise should rule the world; they are very good words," she said.

Speaking to Mrs. Reagan but turning to reporters and cameras, Mrs. Gorbachev said, "I invite you to come to Leningrad and Moscow, because ... we have many historic sights."

If she was impressed by the White House's historic and elegant trappings, she was also circumspect when asked by an American reporter speaking Russian whether she could live in a place like the White House.

"This is an official residence, an official house," she replied through her interpreter. "I would say, humanly speaking, that a human being would like to live in a regular house. This is a museum of American history."

When another reporter asked if she would be able to meet ordinary Americans on her trip, she said time wouldn't permit that. "I would say meeting people is the most interesting thing. I never doubt, and I am confident of the sincere, honest and friendly feelings of the American people."

For that reason, she continued, "meeting you, for me, is meeting Americans. This time our visit is too short. I hope next time will be longer."

She did not hesitate to "meet" those Americans throughout the day, turning to the news media at every opportunity to talk about education, work and her cultural and social views.

Of her efforts to learn English, she said, "We study English at school. Now some 13 million schoolchildren study English. I studied German at school. Some time ago I tried to learn English on my own."

At another point, she talked about the imposition of "duty" on one's free time. "In our age, all of us have to work," she said. "We have professional duties. We have family duties, as well as social duties. A person in the 20th century is at a loss as to how to distribute our time, even though all of us seek to know as much as possible."

At the National Gallery, she said she was "glad to see so many of the staff are women." When it was suggested that she see Georgia O'Keeffe's paintings on her tour, said, "Oh, yes, O'Keeffe, she's a great artist and also, most important, a woman."

She spent some time looking at the photographs of O'Keeffe at the entry to the show. "I told Mrs. Gorbachev that O'Keeffe was a very beautiful woman," Brown said. "And she retorted that all women are beautiful."

According to Brown, Mrs. Gorbachev was surprised at O'Keeffe's mixture of abstraction and realism. "I think she's peculiar," she said, then softened the judgment by saying, "Carter Brown has helped me to understand that talent must find its own face."

She never did get time to view the "American Sampler" show of folk art the welcoming staff had suggested she see.

Brown said that she couldn't pass the sales counters without wanting to know how much everything cost and how many sold. "She also asked if we charged admission and was happy to hear we don't," Brown said. "She wanted the O'Keeffe book right away, and so we had to give away our surprise -- we gave her both the O'Keeffe catalogue and the 'American Sampler's.' "

As Mrs. Gorbachev was leaving the gallery, Occidental Petroleum's Armand Hammer introduced her to ABC superstar Barbara Walters, whom Mrs. Gorbachev invited to "come and see me in Moscow." Walters joked that she was going to hire Hammer as her agent.

After the tour at the White House, Mrs. Gorbachev and Mrs. Reagan retired to the Red Room for coffee and a 25-minute chat, during which, according to a CBS News report last night, "Raisa brought up the homeless and American blacks in a lecturing way, and Mrs. Reagan was not entirely pleased."

Mrs. Reagan's press secretary, Elaine Crispen, said the talk included Mrs. Reagan's antidrug campaign.

"She told Mrs. Gorbachev that she was anxious to learn about the drug problem in Russia," said Elaine Crispen, the first lady's press secretary. "Mrs. Gorbachev said alcohol was the biggest problem they had there, but she did ask Mrs. Reagan if she had any advice as to solutions we have found in this country to drugs." She added that Mrs. Gorbachev was "very receptive."

There appeared to be no competition on the fashion front either, as the two first ladies seemed to be dresed for different occasions.

Mrs. Reagan wore a tailored, brown and beige glen plaid dress by Oscar de la Renta, with a gold choker and gold earrings.

Mrs. Gorbachev was more formally attired in black, from her wool and satin dress to her high-heeled black suede shoes and sheer black stockings with a rhinestone adornment on one ankle. Her belt buckle sparkled like diamonds and at her ears dangled what appeared to be real ones. On one hand was a ring circled with diamonds.

For the NGA tour, she had worn a herringbone suit, with a flared skirt and double-breasted jacket, the same one she wore with a straight skirt for the nuclear arms treaty signing on Tuesday.