The bafflement begins at the beginning. The origins of the affair have been only partially clarified -- the mechanics of what happened are clearer than the motivations.

In spring of 1985, the NSC staff, supported by some CIA analysts, encouraged an opening to the Iranian regime of Ayatollah Ruhollah Khomeini by relaxing the embargo on arms shipments by U.S. allies. It went nowhere after Shultz and Defense Secretary Caspar W. Weinberger pointed out that the proposed shift conflicted with the public policy of not selling arms to a government supporting terrorism.

The situation changed after the June 1985 hijacking of TWA Flight 847 by Islamic extremists and the freeing of its passengers two weeks later. Iranian officials showed willingness to help win the passengers' release. Israeli officials, long interested in pursuing new openings to Iran, proposed to national security adviser McFarlane that a new approach be made to Tehran.

Israel volunteered to take the lead. It would sell Iran U.S.-made weapons as "bona fides" of Washington's serious intentions. Iran would be asked to help gain the release of the remaining six Americans held hostage in Lebanon by pro-Iranian extremists as a demonstration of its good intentions.

This proposal was made to McFarlane by David Kimche, then the director general of the Israeli foreign office. But it was also proposed in other channels. An Iranian arms trader and entrepreneur, Manucher Ghorbanifar, wrote a memorandum for the U.S. government proposing an overture to Iran, including arms for hostages, that he offered to help orchestrate. (Ghorbanifar was already known and distrusted by U.S. intelligence agencies; they suspected he was an Israeli agent.)

Saudi businessman Adnan Khashoggi forwarded Ghorbanifar's proposal to McFarlane. At about the same time, New York businessman John Shaheen, a close personal friend of Casey, was approached by another Iranian-born entrepreneur, Cyrus Hashemi, who had been indicted on charges of illegally selling arms to Iran. Hashemi sought Shaheen's help in avoiding further prosecution, and Shaheen suggested he come up with an idea to improve U.S.-Iranian relations that would include Iran's help in freeing the hostages. Hashemi then proposed helping in an arms-for-hostages deal, according to CIA memoranda.

In August 1985, over continued objections by Shultz and Weinberger, the president gave McFarlane permission to authorize the Israelis to go ahead, with the understanding that the U.S. government would replace Israeli-owned weapons sent to Tehran, according to McFarlane. Former White House chief of staff Donald T. Regan has contended that the president did not give advance approval for the first Israeli shipment. Reagan has said he cannot remember.

The Israelis shipped 100 U.S.-made TOW antitank missiles to Iran at the end of August, then met with Iranian middlemen who agreed that at least one and perhaps more Americans would be released if an additional 400 TOWs were shipped.

In early September 1985, U.S. and Israeli counterterrorism specialists, including North, who worked on counterterrorism for the NSC staff, traveled to Beirut to prepare for a military rescue of the hostages keyed to the anticipated freeing of some of them after Israel delivered 400 more TOWs. It was hoped that U.S. or Israeli intelligence would pick up the movements of the captors as they released the hostage or hostages who were to come out in this swap, then trace them back to their hideout, which could subsequently be raided.

The TOWs were shipped on Sept. 14, and that day the Rev. Benjamin Weir was released. But the tracing plan failed and no rescue was undertaken.

The congressional committees did not publicly explore any aspects of that first Israeli-Iranian deal, including its financial arrangements. The committees did receive financial data that apparently shows which individuals or organizations ended up with the profits from the deal, but the Israeli government provided it on condition that it remain secret.

The committees did release North's notes on the transaction, and they show that the Israelis were paid $5 million, or roughly $10,000 a missile, for 508 TOWs. About $2.2 million went to purchase replacements in the United States in May 1986, according to bank records. Israeli sources say the rest went to Israeli and Iranian middlemen. But that appears to conflict with North's testimony that the middlemen were acting as agents of the Israeli government, and with North's Jan. 7, 1986, notebook entry of a conversation with Amiram Nir of the Israeli government about the August-September TOW deal: "It was agreed the $ {money} was used for other purposes."

If so, was the deal structured from the start to generate money for those "other purposes"? Were these the "joint projects" mentioned by North in a memo to Poindexter in October 1986, which he testified were funded by "residuals" from the arms sales and later described in a closed session to the congressional committees?

On Nov. 14, 1985, North met with his friend Nir, counterterrorism adviser to Israeli Prime Minister Shimon Peres, to discuss, according to his notebook entry, "similar aims, liabilities, vulnerabilities in Leb{anon}." The next 1 1/2 pages of the notebook were blacked out for security reasons before release by the Iran-contra committees. Was there a secret counterterrorism element in the 1986 U.S.-Iran arms deals, modeled on the 1985 Israel-Iran deals, that is being protected even today by various cover stories?The Hawks: Poisoned Fruit?

The next episode of the story -- another shipment of U.S.-made Israeli arms to Iran in November 1985 -- was more fully explored by investigators, but numerous questions remain. The Reagan administration has always shown great sensitivity about its role in this shipment, which was intended to bring home the hostages by Thanksgiving.

The CIA supported the shipment in what amounted to a covert intelligence operation. But there was no written presidential authorization for the agency's action at the time it occurred, as required by law, and Congress was not informed. Like the September shipment of TOWs, this one could easily be seen as a violation of the Arms Export Control Act's restrictions on resale of U.S. weapons owned by foreigners. So the November Hawk shipment was a kind of poisoned fruit that may have set the stage a year later for the president and others to attempt to conceal the U.S. role.

The plan for the November shipment called for a sequence of events: U.S.-made Hawk antiaircraft missiles would be transported to Portugal on an Israeli plane, the hostages would be released and the missiles would then be switched to a non-Israeli aircraft for the flight to Iran.

On Nov. 17, 1985, Portugal refused to clear for landing the Israeli El Al 747 carrying 80 Hawk missiles, and Israeli Defense Minister Yitzhak Rabin called for help from McFarlane, who was then in Geneva for the U.S.-Soviet summit. McFarlane directed North, in Washington, to work on the problem.

North enlisted the assistance of Gen. Secord, then involved at North's direction in setting up an American-operated, secret air resupply operation for the Nicaraguan contras. Secord, and later CIA and State Department officials, were asked to seek Portuguese landing clearances for the Israeli plane.

A variety of approaches, including a call from McFarlane to the Portuguese foreign minister and assistance from the U.S. Embassy in Lisbon, failed to secure clearance. When Lisbon insisted on a written note saying the United States needed its cooperation to help free hostages, the plan to use Lisbon was dropped.

During the negotiations with Portugal, the CIA at North's request arranged for an airplane from one of the "proprietary" companies it controls, St. Lucia Airways, to carry the Hawks into Iran. When a route through Cyprus was later picked for the transfer, North again asked the CIA for help in obtaining landing and overflight rights from countries on the way to Iran, and St. Lucia shipped the weapons as a commercial deal.

On Nov. 20, 1985, the Israelis deposited $1 million in the Secord-controlled Lake Resources account in Switzerland to pay for leasing aircraft from the CIA-owned, commercial company and cover other costs associated with the planned delivery to Iran of 80 Hawks in five shipments.

The first 18 Hawks were flown to Iran on Nov. 25, but the deal took a disastrous turn when the Iranians opened the first crate and found older versions of the missiles -- not even as up-to-date as the ones Iran purchased at least eight years earlier during the reign of the shah.

From his first involvement, North testified, he agreed with the Israelis that the cover story would describe the Hawks as spare parts for "oil-drilling equipment" in the event the operation was disclosed.The 'Finding'

The cover story was known to key decision-makers. Regan testified that McFarlane told him and the president in Geneva about the intention to call the cargo oil-drilling equipment, while making clear that Hawks would be sent.

The Hawk shipment is mentioned on dozens of pages of North's notebooks over a 10-day period; it was discussed in several NSC computer messages, Pentagon memos and, indirectly, in more than 40 CIA cables. These records fully document widespread contemporary knowledge of the actual cargo by U.S. government officials. A North notebook entry for Nov. 26, referring to a 9:40 a.m. meeting with Poindexter, records: "RR {the president} directed op{eration} to proceed."

McFarlane briefed Shultz on the shipment in Geneva, and Shultz dictated a note of this conversation, which was saved. On Nov. 17 the secretary told reporters gathered for the summit that he had a "sense of some motion" with the hostages and had called U.S. Ambassador to Lebanon Reginald Bartholomew to Geneva to discuss the situation with British intermediary Terry Waite. In other words, the administration was preparing for the release of hostages at any moment as a result of the arms shipment.

North's testimony, notebooks and CIA sign-in sheets show that North spent hours with the CIA's Duane (Dewey) Clarridge working on transport of the cargo the weekend before the shipment.

Yet Reagan, McFarlane, Poindexter, North and Clarridge would subsequently maintain that they either could not recollect the Hawk shipment or learned only after the fact that Hawk missiles, not oil-drilling equipment, were the cargo. Last November, when the story of the arms sales began to break, senior officials planned to stick to the oil-equipment story until Shultz and his aides brought up the note he had dictated and refused to go along with the cover story.

Casey was traveling while the CIA was helping to arrange the Hawk shipment, and his deputy, John A. McMahon, was acting director of the agency. McMahon was so concerned about the CIA role in the episode -- performed without benefit of a signed intelligence "finding" from the president to authorize its participation -- that he asked CIA general counsel Stanley Sporkin to draft one.

After learning that weapons had been carried on a plane arranged for and cleared over countries along the route to Iran by the CIA, Sporkin concluded that a finding was required. One was sent to Poindexter Nov. 26 with a note from Casey requesting Reagan's signature. Its scope was unambiguously stated as "Hostage Rescue -- Middle East," and the document stated that, as part of the effort, "certain foreign material and munitions" may be provided to Iran.

Sporkin testified that this finding was unusual for three reasons: It authorized an action that already had occurred; it contained a provision directing Casey not to disclose its contents -- or existence -- to Congress; and it described unambiguously an arms-for-hostages deal.

But the finding, one of only 40 signed by the president during his six years in office, according to Sen. Paul S. Trible Jr. (R-Va.), continued to leave a puzzling trail.

Poindexter testified that Reagan did not sign it until Dec. 5, Poindexter's first day as national security adviser, succeeding McFarlane. Instead of routing the document to a secure file for sensitive NSC documents, Poindexter said he stuck it in his safe. He did not mention the finding to Shultz or Weinberger. Poindexter testified that he forgot about it until last Nov. 21, when, just after attending a meeting at which Reagan asked Meese to look into the November 1985 arms sales it covered, he tore it up -- without, he asserted, informing the president.

Reagan has said that he does not recall seeing or signing the Dec. 5, 1985, finding. He has expressed doubt to aides that the document ever was presented to him, according to White House sources.