Late one night, the dignified, white-haired ambassadors from Mauritius, Radha Krishna Ramphul, found himself down on his hands and knees, crawling about the floor of U.S. Ambassador Andrew Young's apartment.

"We were playing cowboys on the carpet," Ramphul recalls with a chuckle. "Andy's son kept shooting me." Later that night over white wine, however, the two United Nations envoys talked about serious things as well. "This kind of informal exchange," declares Ramphul, "can be very important."

Stories like this abound at the United Nations these days, where Andrew Young is radically changing the world concept of a U.S. ambassador.

Even those celebrated early remarks that led some Americans to wonder how long his old friend Jimmy Carter would put up with him - the off-the-cuff comments about the Cubans being a stabilizing force in Africa, and the British and Swedens being racists - appear to have contributed to Young's succedd.

"Some have questioned his style. Some have said he was being too frank at times - that he was not being 'diplomatic.'" observes Tanzania Ambassador Salim A. Salim. "But I think he had brought a very refreshing type of approach."

"American ambassadors always had this kind of loftiness which the small nations of the Third World used to resent," adds Dramane Ouattara, ambassador of the Organization of African Unity. "They had the type of patronizing attitude that was characteristic of Patrick Moynihan, or the kind of Buddhistic coldness characteristic of John Seali."

Young's personality reflects a dramatic change that has taken place in the past year in Washington's policy toward the United Nations.

Where the Nixon and Ford Administrations tended to view the U.N. as essentially a forum for waging propaganda warfare with the Third World, the Carter Administration has opted to work with the nations that make up a majority of the world body.

The appointment of Young to the U.N. post symbolized this new approach.

"Everyone sees Andrew Young as the perfect antonym of Patrick Moynihan." says Ambassador Mahmoud Mestiti of Tunisia.

"The personal touch - the way he has gone out his way to be friends, to have a personal relationship with the African, Latin American, Eastern European diplomats - has interested everybody," says Ambassador Leslie O. Harriman of Nigeria. "I can assure you now that the United States has more friends all over the world than ever before.

That is not to say that Andrew Young gets uniformly high marks for his first ten months in diplomacy. His casual, some say "happy-go-lucky," style may appeal to much of the Third World, but it grates on the nerves of career envoys of American's more protocol-conscious European allies.

Third World delegations - where Young has scored his most impressive gains - also find plenty to critize in his performance.

"At the beginning particularly, a lot of us felt that he tended to go too much for personal publicity," says Nigeria's Harriman. "Also, he talked from the top of his head."

"A lot of us see him as a one-issue man - Africa," observes the envoys of a major, Middle Eastern country. "Many of us have been struck by his ignorance of such problems as disarmament, and the North-South dialogue."

Even Africans express exasperation over Young's "preconceived ideas" about their continent and are particularly distressed by his constant references to his days in American's civil rights movement.

"I have told him on a number of occasions, you cannot compare the experiences of the civil rights movement in Atlanta with the experiences in South Africa," sighs Tanzania's Ambassador Salim.

But most of Young critics concede that his performance has been improving across the board in recent months.

"Obviously, he's learning." says Nigeria's Harriman. "I notice that these days, he's more careful about his pronouncements. He reads his statements carefully.

"I think he is doing his homework," says Tanzania's Salim. "He knows what hes talking about. Hes not talking nonsense."

Beyond that Third World ambassadors keep coming back to the matter of style. Andy Young, they say repeatedly, is not an "ivory tower" ambassador. Whatever his other pluses or minuses. Young has courted tiny countries that never has so much as a nod in the hallway from a U.S. envoy before - and it clearly matters.

Within hours of being sworn in as U.N. Ambassador, in fact, Young was on his way to the Organization of African Unity's office in New York to meet a group of six African envoys. It was the first time that an American envoy had ever come to them.

"That may not sound important, but it was very important for the people of Africa," says Ouattara. "Moynihan never came to see us. We used to get to see the number two or the number three from the U.S. mission."

Nigeria's Harriman was even more pleasantly surprised when he invited Young out to his official residence in Tarrytown, N.Y., 35 miles from Manhanttan, to meet members of the Committee Against Apartheid - and Young readily accepted. "I could not imagine in previous years being able to get an American ambassador to meet that committee on my home grounds," Harriman says.

In his ten months as U.N. Ambassador, Young has opened up a dialogue with a number of countries and liberation groups that had previously been virtually ignored.

Mfanafuthi Makatini, U.N. representative of the African National Congress, says he had tried unsuccessfully for years to talk to U.S. ambassadors. The closest he came to making contact was a handshake in a U.N. corridor, "I had more or less given up," Makatine says.

At 3 o'clock one morning last week, Makatine found himself seated at the U.S. Ambassador's breakfast table, having a plate of ham and eggs with Young and his family. Observes Makatini: "It's a fresh development."

But for all Young's willingness to meet with - to listen to - virtually anyone, few harbor any illusions that he can turn about American policy overnight.

'Initially, there were people who said, 'Well, now with Young, we'll be able to have a number of more positive policies'," recalls Salim. "Now, they realize that he's not here as Andy Young of Georgia, who was an ally of Martin Luther King. He's here as Andy Young, ambassador of the United States."

Nigeria's Harriman says that after Young vetoed three African resolutions last week that called for sweeping economic as well as military sanctions against South Africa, people asked him: 'Weren't you shocked to see Andrew Young raise his hand to cast those vetoes?"

"We're not such fools," Harriman responds angrily. "Andrew Young might be black, but Andrew Young cannot act except within the frame-work of the foreign policy of his country."

But while Young may not make policy, most of his colleagues at the United Nations believe he strongly influences it - an impression Young fosters with frequent conversational references to his relationship with President Carter.

"When we talk, he mentions, three or four times, 'The President told me,' or 'I told the President'," an Arab envoy says. "everybody knows that Young is in touch with Carter. Everybody's happy about it, because they all want to have somebody here who's in touch with the President."

But has Young's detente with the Third World - a dramatic change from the days when U.S. ambassadors were taking the floor in the United Nations to denounce the "tyranny of the majority" - actually made a difference on any votes? Many delegates say the answer is "Yes."

"This final resolution imposing the arms embargo on South Africa," says the OAU's Ouattara. "We don't like it. But Andy Young did his best. We let it go because of the general effort which has been deployed by people like Andy Young."

Nigeria's Harriman also credits Young's lobbying for the General Assembly's adoption by consensus last week of the toughest U.N. condemnation yet of airline hijacking. Measures like this in the past have traditionally been opposed by a number of Third World countries because of their support for liberation movements.

"But with the gentle words of Andrew Young," says Harriman, "Many of us were able to persuade our friends. "Why should we be awkward about things like this'"

Some Third World delegates, however, have mixed feelings about their warm new relationship with America's U.N. envoy.

"We Africans tend to be sentimental about brotherhood," says the African National Congress's Makatini "Young gets away with a hell of a lot more than Moynihan could ever get away with."

Makatini cited Young's statment a week ago favoring continued U.S. nuclear cooperation with South Africa, adding.

"If that statement had been made by Moynihan, the Africans would have been up in arms."

But for all their doubts and reservations, U.N. diplomats almost unanimously agree that the arrival of Andrew Young has been on balance a net plus.

"As far as Africa is concerned, as far as the Third World is concerned, as far even as the United Nations is concerned," says Tunisia's Mestiri. "I have no doubt about it."