"He can have my job!" the chief spokesman for the president of the United States said of the chief spokesman for the prime minister of Great Britain.

Bernard Ingham, who is to Margaret Thatcher what Marlin Fitzwater is to Ronald Reagan, laughed with gusto.

"I think that all you can say is you do your best in any particular situation," Ingham ventured, skillfully avoiding any direct mention of the particular situation. "I can't comment on an internal American situation at all. I'm not qualified to do that."

It was, in fact, the American situation that brought Ingham and Thatcher to Washington yesterday for a one-day visit. While the prime minister and the president talked nearby in the Oval Office about what Ingham called "the distractions" of that situation, Ingham and Fitzwater renewed an acquaintance that began in London at the 1984 economic summit.

As 20-year veterans of bureaucracy, both Ingham and Fitzwater reached the top in their field through a series of accidental and ambitious moves as government spokesmen.

"I think that we as spokesmen have only one commodity, and that is credibility," Ingham said from his end of Fitzwater's White House couch. "I do wish that the press had to operate against the same stringent criteria of credibility that we have."

Which raised the question of whose credibility concerned him most, his own or Thatcher's.

"Mine, mine, mine," chanted Ingham. "But the two are, in a sense, indivisible, and if you're not credible then quite clearly you're not doing an effective job for your principal. The two are closely linked."

Taking it all in from his end of the couch, Fitzwater graciously surrendered the floor to his visitor. And, Ingham was asked, what is it like having to fashion a silk purse from bad information?

That isn't so much the question, he explained. "But quite frequently in the nature of government you have to try to make a silk purse out of the sow's ear of a situation or, indeed, of a circumstance, because the way of government is not smooth. The way of government is extremely rocky."

Ingham had no idea of how he might handle the Iran-contra problem were he in Fitzwater's job.

"I haven't a clue," he said. Laughing.

Nor would he offer any advice.

"I would not presume to," he said, scrupulously dodging involvement.

"I certainly can use advice," invited Fitzwater.

"You see," Ingham explained, "I think it would be gross arrogance on my part to offer advice to any man in my position in a different country because the systems are different, the people are different, the whole philosophy of life is different. You're made for your own system."

The worst crisis of Ingham's eight years with Thatcher was Britain's war with Argentina over the Falkland Islands in 1982, when the government managed the news, deliberately misleading the media, as was later revealed.

"I said if I come out at the end with any credibility left that would be quite a marvelous thing," Ingham said. "I think I did, but it was very hard work. When you are fighting a war you are concerned above all not to place people's lives at risk. That creates a great strain on how you can operate and you have to find a way of reconciling the safety of your troops with the information that you dispense."

The Falklands war had another effect.

"In terms of domestic policy it dominated everything," Ingham said.

One of the points of Thatcher's visit yesterday was to counsel Reagan against being distracted by the Iran-contra problem and to bolster his image as leader of the western alliance.

"What she's here for is as a loyal ally and good friend, really to say to the president, 'Look, don't allow the problems that are current to distract you from the major issues which are affecting the world, and on which the West and indeed the world needs United States leadership,' " Ingham said.

"They listen to each other," he added.

"I think he listens to her," said Fitzwater, describing Reagan as "in pretty good spirits."

Spokesmen, it seems, know such things because, as Ingham put it, "the first task of a press secretary is to try to get into the mind of the principal and to sort of find the way in which they think and work."

Fitzwater, who moved into the job last February but has worked for the Reagan administration for six years, said, "You get an inner ear -- you can not only hear a voice but you know how it's going to respond. And that's been very important as we go through these contra hearings," he went on, "because the questions I get are, 'What does the president think about ... How does he react to various people?' A lot of it we can't say, and I've talked to him about it, but you have to have a sense because if you don't the press will know fairly soon. You can't be far off for very long."

On memory lapses, both Ingham and Fitzwater confessed to having them.

"I can't even remember what I've said in a briefing," said Ingham. "I mean, one of the things is you concentrate so hard on what you're doing that you can't even remember what you've said."

"I don't remember everything either," echoed Fitzwater.

After 20 years in government, with all the paperwork that comes across the desk, he said, not remembering specific documents is "perfectly understandable."

"Especially," Fitzwater explained, "if the president says, 'I don't remember signing that document but I don't argue with the idea that I did. If I had seen it I would have signed it. I believe in that and that's what I wanted to do.' "

As for the skeptical press, Fitzwater said, "The only thing you can do is be sure you know what you believe, know your principal's {beliefs} and present that point of view. Sometimes the truth is not always readily acceptable."

Said Ingham, describing Thatcher's views on the press:

"The prime minister recognizes that in a democracy you can't have a free society without a free press. But that doesn't say the media should rule your life. What matters more is not what the media thinks, but what is right and what is necessary to do. And you have to argue your case. And she's pretty good at arguing hers."

All that having been said, the spokesmen headed off for a more private conversation.