The Pentagon said yesterday it had finally figured out what happened to those helicopters, the ones with Iraqi defectors aboard that fluttered in and out of existence all week in the Arabian sands.

Nothing happened.

"The Department of Defense can find nothing to confirm those reports, and we do not believe them to be true," Pentagon spokesman Pete Williams said yesterday.

The six Iraqi craft -- two of which, according to the Pentagon's first account, ran out of fuel in the Saudi desert, and four of which landed peacefully at Ra's al Khafji air base -- were figments of an overheated imagination, Williams said. Specifically, he said, the report began when a Marine in the desert "thought he heard helicopters."

In the seven hours it took U.S. Special Operations Command to satisfy itself there was nothing out there, the too-good-to-check story echoed up through the U.S. chain of command and was released to news organizations.

Yesterday's statement, which Williams dearly hoped to be the last in an embarrassing series, completed a neat reversal of the sequence in which spokesmen normally handle awkward news reports. In this case, the confirmation came first, followed by a refusal to confirm or deny, and finally a firm denial.

Nearly everyone wound up with egg on his face. The Saudi government, whose own officials were the first to break the story and the most eager in providing supplementary details, later thundered that the whole thing had been fabricated by foreign reporters. Pentagon officials not only went from confirming the story to denying it, but briefly occupied what Williams called "a kind of middle ground."

Yesterday, for the first time, the official Iraqi News Agency found itself in agreement with the Pentagon. "It never happened," said an agency reporter, who declined to be quoted by name.

What did the episode tell Iraq about the quality of U.S. military intelligence? "It tells me that they are confused," the Iraqi reporter said.

Even yesterday's explanation by Williams did not account for everything learned about the episode during the week.

For instance, how is it that Tuesday's Pentagon intelligence digests, which sources said reported the defections as fact, specifically identified the Iraqi craft as Soviet-built Mi-8 Hips -- a detail not available in any news account? And why did other intelligence reports, according to sources, describe unusual radio traffic between Iraqi aircraft and Saudi pilots or controllers?

Why did a senior official on Wednesday say electronic tracking initially substantiated the Marine's report of helicopters, when Williams said yesterday that nothing was seen flying in the vicinity? Could it be that even yesterday, the Pentagon had something to hide?

If so, one official said, it would be obscured between the lines of the official account. "We lie by not telling you things," the official said. "We don't lie by telling you things that aren't true."