When word of the Iraqi invasion of Kuwait reached the New York offices of ABC News's "Nightline" late on Aug. 1, only 45 minutes remained before the show was to air with a program on lesbian custody. "It was an important issue but no longer germane," recalls Lauren Block, one of the show's four bookers who in a mad scramble somehow managed to locate several Middle East experts and get them into the studio that night.

One of them was Gary Sick, who served on President Carter's National Security Council during the Iranian hostage crisis and who is writing a book on the Iran-Iraq war. Just as important for the desperate Block, this particular expert lives on the Upper West Side, where ABC's studios are located, happened to be home that night and was willing to leap into a cab and make it there in time for an interview.

And since then, it's been one interview after another for Sick and the handful of other Middle East experts who have been besieged by reporters, editors and broadcasters -- all hungry, it seems, for an angle of vision on the unfolding crisis, any scrap of analysis that might have been overlooked by the competition. For the experts, who say they are facing the biggest demand for their wisdom in memory, it's been both burden and bonanza.

"At peak points in the crisis I was getting 50 calls a day, I could have spent my entire day from morning to night doing nothing but interviews," says Sick, who soon began screening his calls in an effort to get at least a little work done on his book. "That first day I wrote an Op-Ed piece for the New York Times, which was obviously done very rapidly. I've been on all the major shows -- 'Nightline,' CNN three or four times, Larry King, 'Good Morning America,' several evening news programs."

It's getting to be a little old hat, actually.

"The first time this happened," Sick recalls, was the week in June 1985 when his book on the Iranian hostage crisis, "All Fall Down," had just come out and the hijacking of TWA Flight 847 by Lebanese Shiite Moslem gunmen suddenly ignited the media. "I thought it was all terribly glamorous and flattering," he says. "I find it less so now. You don't get paid for it. Producers feel it's a public responsibility, and in a sense it is. For anyone like me who's devoted their life to a particular subject, it's nice to be able to express your views to a wide audience."

Nice, too, to be an expert who can command a $3,000 to $4,000 speaker's fee. Sick gives talks at universities for free, but that's what he charges business groups. Like most experts, he also sometimes receives small sums -- $50 or less -- from interviewers in Canada and Europe, where such payments are an accepted practice.

In Washington, Judith Kipper of the Brookings Institution is another expert who appeared on "Nightline" that first night and who, before she left last week for a vacation in Los Angeles, was receiving about 100 calls a day.

"I made the terrible mistake of leaving my forwarding phone number on my answering machine at Brookings," she says, "and I've been getting 20, 30 calls a day out here. If I had 10 cents for every phone call, I'd be able to pay for my rent-a-car. Unfortunately, when they call at 9 in the morning there, it's dawn in Los Angeles."

Kipper doesn't mind, really. She thinks that "people in research organizations have a real obligation to contribute to the public policy debate." And since 1985 she's been a consultant under contract to ABC for an undisclosed sum, advising the network on its Middle East coverage. Her contract doesn't include appearances on the air, she says, which she has made on ABC and CNN.

"This is my 15 minutes of stardom, so to speak," says Kipper, who was at the American Enterprise Institute before Brookings and who once served on the staff of Sen. Robert Kennedy. "Nobody should take it that seriously. A Mideast specialist at a cocktail party, or an AIDS doctor at a cocktail party: It doesn't change anything. There are people who take it seriously and think it changes who they are professionally, or use it as a marketing tool, but in the end I think it's an obligation."

At the Carnegie Endowment for International Peace, another Middle East expert, Geoffrey Kemp, had a personal reason to be upset with developments in the gulf region. "I was about to go to the printers with a 350-page book on the need for arms control in the Middle East," he says with a sigh, "and thanks to Saddam Hussein the whole bloody thing has got to be reworked."

Currently in Tel Aviv for what he calls "private consultations," Kemp, who was senior director for the Near East and South Asia on the NSC in the first Reagan administration, says he received close to 400 telephone messages from the media during the first three days of the crisis.

"It was like being back in the White House again," he says. "This is more serious than the other Middle East crises. The phone never stopped, you're constantly listening to the top of the news. People call at all hours from around the globe. It was heady stuff for three or four days, then I wanted to get out of town."

He was on CBS and ABC, on CNN several times, "and I've done dozens of foreign broadcasts. What is very interesting is how a lot of the journalists who cover the news, particularly the print media, are extremely knowledgeable about the subject. Sometimes one is just kidding oneself that they're calling for your expert opinion. They're calling to get what they want to write, and they're looking for quotes that fit."

Kemp is looking, among other things, to see if any new experts emerge from this crisis. "You see the old standbys," he says, "but in every crisis someone new turns up. What's really different about this one is that it involves the U.S. military, so you have a whole new area of people who know about chemical weapons and rapid deployments."

One of these is Eliot A. Cohen, only 34, a whiz kid in military strategy out of Harvard via the Naval War College in Newport, R.I., and who now hangs his hat at the Paul H. Nitze School of Advanced International Studies of the Johns Hopkins University in Washington, where he is a full professor. Despite all these accomplishments, he's in a state of amazement.

"It's the first time I've really been thrown into the middle of this kind of thing," he says of the crisis and the demand for his views. "What's striking is how easy it is for people to get hold of you in Washington. It's a little unsettling to realize that a lot of the phone calls are because of convenience. You're available. The studios are right down the street."

And the temptation, too, is right handy. "Let's face it, most of us {experts} don't know that much more than anybody else who's reading the newspaper," he says. "What you can do is try to put it into a larger perspective. But it would be easy to do more of this than one really should. It makes me a bit uneasy, frankly, the temptation to become a blowhard, or a pundit."

Even though he is new in town, he received at least 50 media calls during the first week of the crisis. "It's all very exciting and so forth, but it's too easy to get away from doing serious, scholarly work," he says. "It wears thin pretty quickly."

Nevertheless, he can't help but say, "It's been a big thrill for my mother, seeing me on TV."