Shortly after 10:15 p.m. Thursday, an Egyptian 737 airliner lifted off the runway at Cairo East airport and wheeled westward. The takeoff seemed routine, but appearances were deceptive. The plane's tail number was relayed instantly through intelligence channels to American F14 Tomcat fighters circling as they waited in ambush over the dark Mediterranean.

Two hours earlier (8:15 Egyptian time, 2:15 p.m. EDT), seven Tomcats accompanied by four aerial tankers and two sophisticated communication planes had vaulted into the wind from the deck of the carrier USS Saratoga, cruising off the coast of Albania, on a mission that had been launched 6,000 miles away at the Sara Lee bakery in Deerfield, Ill. President Reagan, preparing to promote his tax-overhaul plan, had briefly paused in a private room at the bakery around 1 p.m. EDT, to confer with Robert C. McFarlane.

The national security affairs adviser had urgent news: Four pirates who had hijacked the Italian cruise ship Achille Lauro and murdered an elderly, crippled American were still in Egypt, despite repeated claims by Egyptian President Hosni Mubarak and his aides that they had left the country.

McFarlane wanted Reagan to approve a dramatic scheme to intercept the Boeing 737 preparing to whisk the terrorists to freedom.

Reagan agreed in principle, but only if American pilots were certain they could identify the correct plane. He said he would withhold final approval to intercept the 737 until he had detailed information on the target of the proposed U.S. action.

In retrospect, the die was cast. Mounting frustration at being repeatedly victimized by international thugs, coupled with the president's 5-year-old vow of "swift and effective retribution," led Reagan to approve a stunningly successful military operation culminating in the killers' capture on the island of Sicily less than eight hours later.

The capture was a triumph for U.S. intelligence and military prowess in an age when both had been questioned, even ridiculed. Possibly with Israeli assistance, a knowledgeable intelligence source said yesterday, "We knew all the time where the hijackers were located." Other sources said the United States gathered valuable intelligence by electronically eavesdropping on a debate between Egyptian factions bickering about what to do with the terrorists.

Even in triumph, there were moments of anxiety and, briefly, one near-firefight with Italian forces. Upon reaching the NATO air base at Sigonella on Sicily, the four Tomcats and the Egypt Air 737 were forced to circle the runway until the flabbergasted air traffic controller was assured by Rome that the mysterious visitors were authorized to land.

On the tarmac the plane was surrounded by forces that included Delta Force commandos, who had been flown earlier in the week from Fort Bragg, N.C., to the amphibious assault ship USS Iwo Jima for a possible attack on the Achille Lauro. Later, they had been moved to Sicily where they greeted the 737, rifles ready.

But Italian carabinieri, also on the scene, insisted that the Americans give way. Finally, after what one intelligence source described as a confrontation that nearly led to gunfire, the U.S. troops ceded control of the hijackers and two other Palestinians aboard the plane.

The dramatic climax to the saga of the Achille Lauro had begun Thursday morning as Reagan was preparing to leave the White House for Chicago.

The discovery by U.S. intelligence, apparently through satellites and spies, that the four Palestinians were still in Cairo presented the administration with one of its toughest decisions of the decade: whether to risk a diplomatic rupture with one of Washington's closest Arab allies or allow yet another terrorist gang to flee.

Despite Mubarak's insistence that the hijackers were gone, U.S. intelligence officials and the White House were convinced the claim was false. Though uncertain where the terrorists were precisely, they were sure they had not left Egypt; some thought the hijackers wanted to fly to Tunisia.

The location of the terrorists was the critical part of a puzzle that McFarlane was trying to piece together as he flew with Reagan in Air Force One to Chicago. Finding the hijackers was vital because, as one White House official recalled yesterday, they were fearful that, for the second time this year, the "cold-blooded killers" of an American would "get off scot-free." The memory of hijacked TWA Flight 847 was painfully fresh.

Despite the intelligence reports, confusion was rampant. "We were getting reports of first one thing, then another," White House chief of staff Donald T. Regan recalled.

Reagan did not help matters when he paused to field questions in a light rain at Chicago's O'Hare International Airport. After expressing his outrage at the murder of American passenger Leon Klinghoffer, the president appeared to grope for words as he suggested that he would approve if the hijackers were prosecuted by the Palestine Liberation Organization. His advisers instantly recognized the gaffe, since the United States has never recognized the PLO, and McFarlane corrected the president.

By the time he reached the Kitchens of Sara Lee, Reagan had revised his position, demanding that the Palestinians be put into the hands of a "sovereign nation."

But there was still confusion over the larger issue: how to block the terrorists' flight to Tunisia. McFarlane spent much of his day on the phone to his deputy in Washington, Vice Adm. John Poindexter, who had become point man for the White House crisis team. They were particularly vexed by contradictory reports of the plane's destination.

"During the day," McFarlane said yesterday, "we'd receive reports that we expect that it will leave at X hour from Y place and go to Z final point. And that changed occasionally."

No one seem more baffled than Reagan, who told reporters at the bakery, "All I know is they're off the boat and they're some place over there and our people are safe." Mubarak, he suggested, might not have "the information he should have."

McFarlane said that even before this episode Reagan had given standing orders to maintain military "readiness" in case of a terrorist attack like the hijacking of the Achille Lauro. This included "readiness to surveil, to track, to apprehend."

When it appeared the Egyptian plane might leave Cairo, plans were laid in Washington to "divert" the airliner, McFarlane said. Other officials said Pentagon and National Security Council officials prepared the plan to "locate, intercept, positively identify and escort" the Egyptian aircraft to the air base in Sicily.

Part of the process of narrowing down the location of the Egyptian plane was guesswork, officials said. They knew there were narrow options available to the hijackers. Libya was apparently ruled out because of bad blood between Mubarak and Libyan leader Muammar Qaddafi.

A flight to Iraq and other Arab countries to the east was considered too risky because of the potential for interception by Israeli warplanes. That effectively shrank the list of possible sanctuary countries to Tunisia, Algeria or possibly some other Mediterranean nation like Greece.

Before the plane left Cairo, Reagan approved the U.S. plan in principle, including the so-called secret "rules of engagement" governing the nocturnal flight. A senior U.S. official suggested yesterday that those rules would have prohibited the American fighters from shooting down the civilian airliner, although U.S. officials have deliberately left the question open to confuse terrorists.

McFarlane said Reagan approved three points: that the interception should be attempted, that "certain precise rules" should be followed, and that it not take place until the military reports back on "actual movements" of the Egyptian airliner.

That movement became the next hurdle. "There was never certitude that it would occur at a certain time," McFarlane said.

Reagan's approval of the plan raised delicate diplomatic problems. Egypt is among the foremost Arab allies of the United States. Officials said they recognized Mubarak was in a jam. To extradite or imprison the hijackers, perhaps even to identify their location to the United States, could spark a severe reaction from Palestinian sympathizers and Moslem fundamentalists in Egypt, damaging Egypt's efforts to reassert itself as a leader in the Arab world.

But to let the hijackers go, now that it had become known they were killers, could deal an irreversible blow to Egypt's standing in the United States and end its hopes of continuing as the second-largest recipient of U.S. foreign aid.

U.S. officials figured that Mubarak was trying to steer between "a rock and a hard place," as one put it. Senior officials said they had a choice of either looking the other way as Mubarak tried to get the hijackers out, or going after the hijackers immediately and worrying about Egyptian relations later.

They decided to go after the hijackers. Asked about the possible damage to the Middle East peace process, McFarlane said yesterday, "That was discussed . . . . It never reached a point where the risks exceeded the potential gains."

When the Egyptian plane did take off, Reagan was on his way back to Washington. He gave the final order for the interception to McFarlane on Air Force One after speaking by telephone with Defense Secretary Caspar W. Weinberger.

The aircraft carrier Saratoga, which normally carries about 70 warplanes, had turned south from the coast of Albania where it had been heading for a scheduled port call in Dubrovnik. Its fighters had been armed and on alert almost since the beginning of the ship hijacking ordeal.

When Reagan had given the first approval in Chicago, the ship launched the F14s. Typically, each would have been armed with a two pairs of Sidewinder and Sparrow air-to-air missiles.

The fighters, eventually joined by their support planes, headed south of Crete and loitered for three hours. While waiting in the dark for orders from Reagan and the arrival of the Egyptian airliner, the fighters had to be refueled several times.

In addition to the far-seeing radars of the E2Cs and the F14s, the strike force was supported by Navy and Air Force intelligence planes based in Spain and Greece. In addition, the USS Yorktown, an Aegis cruiser equipped with the Navy's most advanced radar, accompanied the Saratoga and provided important information on air traffic over the Mediterranean.

At 4:15 p.m. eastern time, the Egyptian civilian airliner with the four Palestinians involved in the shipjacking accompanied by two other Palestinians and four Egyptians took off east of Cairo. U.S. military officials watched and listened to the plane's radio communications from the moment it took to the air.

As the Egyptian airliner left Egyptian airspace and headed west over the Mediterranean, four F14s -- their lights extinguished -- boxed the commercial jet while three other U.S. interceptors trailed behind. The Egyptian pilot was not aware that he had been surrounded, Pentagon officials said.

The civilian pilot, who was using standard commercial radio channels, asked Tunisia for permission to land. But U.S. officials had asked the Tunisian government to turn away the 737. The Tunisians complied.

As U.S. Navy crews in the E2C surveillance plane eavesdropped, the Egyptian pilot radioed Athens for permission to land but was rebuffed again. At that point, the intercept began.

The E2Cs used voice radio communications and radar contact while the F14s moved in, flashing their lights to convince the Egyptian pilot he was surrounded. The Navy crews ordered the 737 to follow them to Sigonella.

Some officials reported yesterday that the plane was changing course as the interception began and that its pilot initially seemed to be resisting the U.S. commands. But several defense officials said that the pilot complied without argument.

Italian sources also reported that the United States initially sought to divert the Egyptian jet to a U.S. Air Force base near Frankfurt, West Germany, where the U.S. government could be certain of controlling the Palestinians' fate. But U.S. officials insisted that Sigonella was the goal from the start.

When the 737 finally touched down, the jetliner startled its escorts by immediately taking off again, apparently because the pilot mistakenly believed he had run out of runway space.

But the F14s, still on his flanks, watched as the Egyptian pilot circled the field and returned for a smooth landing. U.S. commandos, Italian soldiers and carabinieri surrounded the captured 737. The U.S. interceptors circled overhead until they were assured that the Egyptian jetliner was in custody, officials said, then they headed back to the Saratoga.

One well-placed intelligence source said that the U.S. and Italian troops were jockeying for control on the ground, with the U.S. commandos initially refusing to give way until the Italians promised to extradite the four shipjackers. But the Italians insisted on taking the four into custody, and they eventually won out.

The commandos were part of a Delta Force strike team that the Pentagon had sent from Fort Bragg, N.C., to the Mediterranean while the Palestinians still had control of the Achille Lauro, according to senior defense sources. Some of the Navy SEALs and Army special forces had been flown by helicopter to the Iwo Jima in case Reagan had ordered a strike mission to recapture the pirated vessel.

After Reagan returned to Washington he visited the White House physician's office to have minor cancer surgery on his nose. McFarlane flew to New York to meet with former President Richard M. Nixon to discuss foreign affairs. Poindexter monitored events from the White House situation room. There was a sense of anxiety there until word came that the operation had been a success, one official recalled.

Once the Egyptian plane had landed, however, "there were a lot of thumbs up around here," the official said. Reagan learned of the successful intercept in a telephone call from Poindexter.

Then White House officials went to work drafting a statement that would acknowledge the differences with Egypt but also attempt to smooth over any damage caused by the interception. McFarlane returned from New York at 11 p.m. just as White House spokesman Larry Speakes was preparing to read the announcement to television cameras.

In the aftermath of the incident, officials launched an immediate campaign to repair relations with Egypt. They agreed to say as little as possible about the Egyptian role, avoiding recriminations or charges that the Egyptians had lied. The officials said that pro-Israel lobbying groups had agreed with the administration that no purpose would be served by "Egypt-bashing."

Yesterday, McFarlane refused to criticize Egypt. Mubarak, he said, "was acting on his own set of facts, and I wouldn't second-guess that."

The bipartisan enthusiasm for the interception was perhaps best captured by Sen. Daniel Patrick Moynihan (D-N.Y.), who crowed, "Thank God we've won one."