The first interdepartmental foreign policy study ordered by the incoming Reagan administration early this year considered what the United States should do to oppose Libya and its militant, unconventional leader, Col. Muammar Qaddafi. A few months later, authoritative sources reported that the administration had drawn up plans to "make life uncomfortable," at a minimum, for the leader of radical Libya.

With this background, on top of several years of increasing bitterness and cross-purposes between the two governments, yesterday's aerial clash in the Mediterranean was not a surprise that came out of the blue. Nor is there much chance, in the opinion of Washington officials, that it will be the last episode in the confrontation between the United States and its third largest overseas oil supplier.

Nobody can predict with certainty what will come next, for that depends as much on Libya as on the United States. Government officials expressed doubt yesterday that Libya will terminate its lucrative oil sales to the United States because of the incident, but there are certain to be major diplomatic and political consequences in Africa and the Middle East.

A further military clash is not ruled out. Libya's close relations with the Soviet Union, which was quickly notified of the clash early yesterday by the State Department, adds a potential superpower dimension.

Moreover, administration officials do not take lightly the public threat from Libya Aug. 13, attributed to "Free Unionist Officers" there, to respond to any harm to Qaddafi by striking "U.S. interests anywhere" and seeking "the physical liquidation" of Americans, beginning with President Reagan, whether overseas or in Libya.

The State Department has publicly denied press reports of a U.S. decision to assassinate Qaddafi. Perhaps because of the suggestions of physical danger, Qaddafi is reported to be under reinforced security wherever he goes.

When Algeria's President Chadli Bendjedid postponed a trip to Tripoli because of the impending U.S. naval exercise off the coast, according to U.S. intelligence, Qaddafi cautiously left Libya before the naval maneuvers began, arriving earlier than expected at a meeting in Aden, South Yemen. There Qaddafi signed a Libyan-Ethiopian-South Yemen "friendship and cooperation treaty" yesterday, which is described by Washington sources as a Libyan-bankrolled pact to confront American-allied countries in the area.

The roots of U.S.-Libyan conflict go back many years to the avowedly radical policies of Qaddafi, leader of a group of officers who overthrew the Libyan monarchy in late 1969. The discord has grown rapidly in the past several years, especially after the U.S. Embassy in Tripoli was sacked and burned in December, 1979, by a Libyan mob that American officials charged had government blessing.

In an earlier incident strikingly similar to yesterday's, a U.S. Air Force ED135 electronic eavesdropping plane flying at the edge of Libyan airspace last Sept. 16 reportedly was fired upon with missiles by two Libyan fighter planes. The Air Force crew did not see the missiles or the planes, but U.S. radio intercepts picked up the orders to fire emanating from ground control, according to Washington Post Pentagon correspondent George C. Wilson.

Tbe Carter administration did not announce the incident nor lodge any public protest but it ordered increased protection for its eavesdroppers. A few days later Navy F14 fighters chased away a group of challenging Libyan warplanes, Wilson reported at the time.

The Reagan administration has taken a more strongly confrontational position about Libya from the very start. In his first news conference eight days after taking office, Secretary of State Alexander M. Haig Jr. called Libya's incursion into the African country of Chad "a grave turn of events" and said it was being "very, very carefully" considered. Later the administration denounced "Libya's policy of international terrorism and subversion" and declared that "the ultimate objective" of U.S. policy is to change it.

As secret interagency studies of "the Libya problem" got under way, Haig was reported to have rejected an early report from within the State Department setting forth the substantial risks to Americans and American policies of taking direct action against Libya. The secretary wanted a tougher and more positive reponse, officials said.

In the spring of 1980, the Carter administration expelled four Libyan diplomats on suspicion of threatening anti-Qaddafi Libyans residing in this country. This May 5, just a year later, the United States expelled the remaining Libyan diplomats, more than 20 in all, because of what it called "Libyan provocations and misconduct, including support for international terrorism."

At the same time, the United States withdrew its remaining diplomatic personnel from Libya, warned Americans not to travel to that country and advised all private Americans there, numbering more than 2,000, to leave. U.S. oil companies, the principal employer of Americans in Libya, have reduced the numbers of U.S. personnel and dependents there to about 1,200 but have been reluctant to go further for economic reasons.

The Wall Street Journal, in a July l4 story, said that repeated warnings to oil companies to remove their people right away was "a clear indication that something sensitive is brewing." The newspaper quoted an unnamed U.S. official as saying "the companies won't get another warning. We're playing confrontation politics, and we want them out, whether there is a coup in the works or not."

Haig on May 29 declared publicly that Libya's oil revenues are "almost exclusively diverted to the purchase of armaments, the training of international terrorists and the conduct of direct interventionism in the neighboring states of northern Africa, the most recent of which being the invasion of Chad."

Chester A. Crocker, the assistant secretary in charge of African affairs, declared on June 2 at a State Department foreign policy conference that the United States would support all African nations that want to resist "interventionism" from Libya.

Crocker, in Senate Foreign Relations Committee testimony July 8, set out the administration's view: "Under Col. Qaddafi, Libya has adopted a diplomacy of subversion in Africa and the Arab world. It is a diplomacy of unprecedented obstruction to our own interests and objectives. Qaddafi has tried in every way he could think of to obstruct our efforts to achieve peace in the Middle East. He has sponsored subversion from Africa to the Philippines. He has actively supported international terrorism, using assassinations abroad as an instrument of his policy."

Other U.S. activities regarding Libya under the Reagan administration have included:

Diplomatic appeals at almost every level to friendly countries to join in isolating and condemning Qaddafi. Among those with whom this was discussed were Western European foreign ministers, some of whom advised caution lest an overt U.S. campaign strengthen Qaddafi at home and in the Third World.

Libya was an important topic in the talks two weeks ago between Reagan and Egyptian President Anwar Sadat, according to participants in the meetings. Sadat, who has long opposed Qaddafi and often describes him as "a lunatic," is reported to have taken the view that Libyans inside that country, rather than overt pressures from the outside, are the most effective opposition. This view may have reflected a reluctance on the part of Sadat to confront Libya militarily now.

Stepped up U.S. aid to neighbors of Libya. The administration has asked for major increases in military assistance for Tunisia, Sudan and Egypt, all of which border on Libya. A plan to sell M60 tanks to Tunisia "in order to deter further Libyan adventurism" was announced by the State Department last month.

On a trip to the area in June, Deputy Secretary of Defense Frank Carlucci discussed additional U.S. military sales and support with leaders of Tunisia, Morocco, Sudan, Egypt and Algeria. Aides said Libya was discussed.

The recent naval exercise, which was seen from the first as likely to draw a reaction and perhaps a physical response from Qaddafi. The exercise was the subject of intensive Defense Department discussions, in which other departments and agencies joined, last month. Reagan himself is reported to have given the final go-ahead in a National Security Council meeting.

Newsweek magazine's "Periscope" column, in the issue printed last weekend, referred to the naval maneuvers as the Reagan administration's "first direct challenge to the Libyan strongman Qaddafi " after "months of debating how to neutralize" him. The magazine pointed out that Libya claims that the maneuvers area is Libyan territory, but that the United States does not recognize this claim. The account went on to say that the naval maneuvers "will test Qaddafi's reactions -- and those of his allies in Moscow."

According to some accounts, a plan involving the Central Intelligence Agency and other U.S. resources to oust Qaddafi and reverse Libyan policy. Sources available to The Post denied that it was an assassination plot, describing the plan as a long-range enterprise which concentrated on placing pressures on Qaddafi from outside his country.

Libya's "Popular Committtee of the People's Bureau for Foreign Liaison," in effect, the Libyan Foreign Ministry, protested U.S. activities in a diplomatic note to the United Nations Security Council published Aug. 4. The note charged that "the U.S. government has been escalating its campaign" against Libya "with the aim of preparing the atmosphere to embark directly or via its agents upon a hostile action."

The Libyan protest singled out the announcement of U.S. readiness to increase its military aid to neighbors of Libya, "the escalation of a U.S. propaganda campaign . . . for the purpose of preparing U.S. and world opinion to accept any aggression by the United States or any of its agents in the area" and "the spread of reports" about a covert action plan to kill Qaddafi.

At 12:48 p.m. Tuesday, about 12 hours prior to the military action between the United States and Libya, the official Jamahiriyah News Agency reported the Newsweek Periscope item in an English-language dispatch. As monitored by the U.S. government, the Libyan news agency quoted its unnamed "political editor" as saying the maneuvers "expose the nature and reality of American aggressive intentions." The official was quoted as saying, "The Libyan Arab people, faced with this provocative armed stance against its revolution and leader, will fight by all means for its territorial waters and any inch of its land or air space whoever is the aggressor party, whether it is America or any other force."

About two hours later, at 2:15 p.m. Washington time Tuesday, Tripoli radio, in a broadcast monitored by U.S. services, called the naval maneuvers "a violation of national sovereignty" and said Libya "reserves the right to take all measures that it sees necessary to safeguard its legitimate rights in its airspace and territorial waters."