While Soviet leader Mikhail Gorbachev was posing for photographers with President Reagan outside the Soviet mission today, an American reporter shouted a question at him about women and whether they are interested in the complicated issues of nuclear missiles and arms control.

Gorbachev's Soviet interpreter repeated the question in Russian, but Gorbachev looked puzzled and a little taken aback.

He summoned a veteran U.S. interpreter, William D. Krimer, to get a better understanding of the question, and then launched into a long response that both men and women "are interested in having peace for themselves."

The incident underscores the immense importance of the interpreters who have been present here in the long, private meetings between Reagan and Gorbachev. They are not only critical to the talks, but also are laying down a remarkable historical record of the private meetings between the two leaders.

The record is important because in the past there have been instances of misunderstandings on critical issues at summit meetings, and without a complete record it would be more difficult, if not impossible, to resolve them.

Although it is not widely known, the White House has used the interpreters to make a nearly verbatim transcript of the private conversations between Reagan and Gorbachev. The transcripts, produced quickly here, are seen by only a handful of top officials and kept secret from others.

"It's same-day laundry service," a White House official said. "We know exactly what was said."

But the record of the private talks is not cross-checked with the Soviets, who presumably are making a similar history.

As the Geneva summit was originally planned, Reagan and Gorbachev were to spend most of their time at formal plenary sessions, attended by six advisers. On the U.S. side, one of those advisers, John F. Matlock Jr. of the National Security Council, is fluent in Russian. Also present would be official notetakers and interpreters. The notetakers would record the conversations for immediate reference and historical analysis.

But the president shifted the emphasis of the summit from the formal sessions to the one-on-one private meetings. Two such private sessions were held yesterday -- including one in the seclusion of a private pool house at the Swiss chateau Reagan was using -- and two more today at the Soviet mission, including a 90-minute standing chat in the grand hall of the mission.

The leaders spent more time over two days in private talks than in formal session. Nearly five hours were consumed in the one-on-one meetings out of the total nine hours of discussions.

These talks have become the unexpected highlight of the summit, and except for Reagan and Gorbachev, only the interpreters have been present. They remain at the leaders' elbows, providing consecutive translation. This means that when, for example, Reagan speaks to Gorbachev, his words are translated in Russian to the Soviet leader before Gorbachev answers. The process is reversed when Gorbachev speaks.

By contrast, in the formal meetings, the words are translated simultaneously and listened to through headphones.

The interpreters take notes before relating each exchange, and these notes are the basis for informing U.S. officials of what was said. The U.S. interpreters are State Department employes, and they are not free to talk about what they've heard. "My mouth is sealed," Dimitry Zarechnak, 41, responded today when asked how the talks are going.

Zarechnak, who attended the 1972 summit as a U.S. interpreter, said he was born in Czechoslovakia and came to the United States at age 4. He accompanied Shultz on his recent trip to Moscow, and recalled today that Gorbachev interrupted him at one point in those discussions to ask where he was from. He told Gorbachev, he said, that his father came from the Carpathians and Gorbachev responded that his own father "had died there during the war."

In addition to the interpreters' notes, Reagan is also telling his advisers what he recalls from the talks. White House spokesman Larry Speakes said Reagan is working from memory and is not taking any notes of his own. Reagan is giving his account to Chief of Staff Donald T. Regan, national security adviser Robert C. McFarlane and Secretary of State George P. Shultz, Speakes said.

"I don't think either side has any problems with recollections of the meeting being properly recalled for future use," Speakes said today, adding that there is an "adequate historical, political and diplomatic record."

The importance of this was demonstrated in 1979 at Jimmy Carter's Vienna summit with Leonid Brezhnev. By prior agreement, both sides were supposed to read statements into the record about limits on strategic arms, but Brezhnev made an evasive comment about the Soviet Backfire bomber. Carter brought this up the next day and insisted on a more precise statement, which he eventually got.

A similar episode occurred in 1972 at Richard Nixon's meeting with Brezhnev in Moscow. Helmut Sonnenfeldt of the Brookings Institution, who was a notetaker at that summit, recalls that he spent three hours in a meeting at which the leaders were trying to negotiate increases in silo sizes for intercontinental ballistic missiles.

"It would make a terrific musical comedy," he recalled. "I didn't know what the hell they were talking about. It was three hours wasted. It was eventually dealt with at the expert level . . . . It may have done other things for them . . . but it didn't do anything about silo sizes."

A senior administration official in the Reagan administration took note of that episode this week, recalling that Nixon and Brezhnev had agreed to increase silo sizes by 10 to 15 percent, but did not specify whether it would be the diameter or depth or both.