There was a moment in the Achille Lauro affair that seemed to sum up both the successes and the frustrations of U.S. diplomacy and military power.

Last Saturday evening, the U.S. aircraft carrier Saratoga was lying at anchor in the Yugoslav port of Dubrovnik on a symbolic good-will visit to the first Communist country to break away from the Soviet Bloc. Tucked away on its hangar deck were the F14 fighters that, just a few hours before, had forced the landing in Sicily of an Egyptair plane carrying the suspected murderers of an elderly American tourist on the Italian cruise ship.

The welcoming festivities for the giant aircraft carrier had scarcely gotten underway when a Yugoslav airliner on the Rome-Belgrade route flew almost directly overhead, landing at Dubrovnik airport. On board was Mohammed Abbas, a senior Palestine Liberation Organization official accused by the Reagan administration of masterminding the hijacking of the Achille Lauro.

Abbas, traveling (according to fellow passengers on the plane) on an Iraqi diplomatic passport under an assumed name, had been scooped up in the Egyptair catch and subsequently released by the Italian government. At this precise moment, thanks to a deal worked out by Italy, Yugoslavia and the PLO, he was en route to a new hiding place, out of the clutches of U.S. authorities.

The incident and the mixture of anger and embarrassment it has helped to generate provide a good illustration of the practical difficulties faced by the Reagan administration in pursuing its declared aim of waging war on terrorists. It also highlights the political dilemma facing Yugoslavia, which has sought to preserve its prestige in the nonaligned world at the same time it promotes good relations with the United States.

The story of Abbas' flight to freedom has demonstrated that national interests and realpolitik frequently pose obstacles to effective cooperation on terrorism.

During the past two days, Yugoslav and U.S. officials here have tried to protect the long-term relationship between Washington and Belgrade from what they evidently view as the transitory diplomatic havoc created by Abbas.

From the American point of view, Yugoslavia occupies a strategically important position between East and West that Washington has every interest in denying to the Soviet Union. U.S. officials also appreciate Yugoslavia's moderating influence in the Nonaligned Movement, where it acts as a political counterweight to pro-Soviet states such as Cuba and Vietnam.

The sensitivity of the Abbas affair for U.S.-Yugoslav relations was reflected in a blanket refusal of senior U.S. diplomats here to discuss the subject with journalists. Inquiries were referred to the embassy press office for a routine "no comment."

According to non-American diplomatic sources, U.S. Ambassador John D. Scanlon held an urgent meeting with Yugoslav Foreign Ministry officials Sunday after hastily returning to Belgrade from welcoming the USS Saratoga in Dubrovnik.

From the Yugoslav point of view, Washington's good will is vital if the country is to get out of its deep financial and economic crisis. At the instigation of former State Department official, Lawrence W. Eagleburger, who served as ambassador to Belgrade from 1977 to 1981, the Reagan administration has played a leading role persuading western banks and other western governments to roll over nearly $20 billion in accumulated debts.

Yugoslavia is also vulnerable to U.S. retaliation on the extradition front, as Washington must soon make a decision on the case of a former Croatian war criminal wanted by Belgrade. Courts in Los Angeles approved the extradition of Andrija Artukovic, who is accused of ordering the slaughter of millions of Serbs, after a 40-year campaign by Yugoslavia for him to be handed over.

Yugoslav leaders have also tried to mend fences with the United States by blocking a press conference scheduled for Abbas on Monday and hustling him out of the country. A statement promised by Belgrade on its reasons for ignoring urgent U.S. demands for the PLO official's arrest has been delayed in the hope that tensions will subside.

In private, Yugoslav officials have sought to play down the significance of their decision to allow Abbas into the country by insisting that he was only here "in transit." Assuming that he did leave on Monday morning, as the PLO said, his total stay was less than 48 hours.

Once Abbas had arrived in Belgrade, Yugoslavia's nonaligned status and close relations with the PLO made the decision not to hand him over to Washington predictable. A larger mystery for usually well-informed Yugoslav analysts is why the government risked so much by admitting him in the first place.

"It would have been quite possible for us to have wriggled out of this without attracting attention to ourselves," a Yugoslav journalist said.

One line of speculation was that the Yugoslav government was not fully aware of the potential diplomatic repercussions when approached by Italy and the PLO to provide safe passage for Abbas.

As a member of the PLO's 12-man Executive Committee, which is recognized as the sole legitimate representative of the Palestinian people by Yugoslavia, Abbas enjoyed a certain diplomatic status here. Yugoslav officials were further reassured by the fact that Italy, a U.S. military ally, announced that it had no grounds for holding the PLO leader.