Striding across the marble hotel lobby, the American Farm Bureau delegate shifts his eyes uneasily, glancing beyond his Stetson brim at Iran's Mullah Mohammed Montazari.

Both are guests of the Arab world's mercurial Hotspur and radical political outrider, Col. Muammar Qaddafi.

This juxtaposition of mid-American agribusiness entrepreneur and revolutionary mullah symbolizes the contradictory, scrambled and often illogical relations the United States has with its third largest supplier of foreign oil.

Libya: Haven for deposed Ugandan dictator Idi Amin, coziest Soviet friend in the oil cartel and an earnest customer for billions of dollars worth of Moscow's most advanced weaponry, arms supplier and financial backer for a broad array of revolutionary movements and terrorist groups.

Libya's image as bankroller of international terrorism is one that it has done much to deserve. But there is another side to Qaddafi's Libya, one that intimately links it to the United States through the medium of oil and pours U.S. petrodollars into Libyan coffers.

Third largest foreign oil supplier for the United States, Libya sells U.S. companies 40 percent of the 2 million barrels it exports daily - more than the United States received from Iran at the peak of American relations with the shah. Libyan oil, moreover, "is highly prized - and priced - "sweet" crude that is easily and profitably refined into gasoline.

The U.S.-Libyan oil connection will mean more than $5 billion to Qaddafi this year and has engendered an intricate web of relations between American companies and banks and Libya's maverick government.

Libyan ambassador to the United Nations Mansour Elkikhia cloaks the ties in diplomatic understatement, calling it a "peculiar relationship" that at the same time both binds and separates Washington and Tripoli.

Farm Bureau head Allen Grant, between negotiations on a $30 million agricultural project:

"There are good prospects for American business here." It is a view shared by a cluster of Fortune 500 corporations.

Mullah Montazari at the start of a three-hour press conference in Tripoli: Iran, like Libya, is "ready to fight dictatorships of every kind, including Saudi Arabia," America's close ally and chief oil supplier.He ends with a bristling attack on the United States.

The "peculiar relationship" now is undergoing some of its severest strains in the 10 years since Qaddafi's nearly bloodless putsch ended a generation of docile American clientship under the Libyan monarchy of King Idris.

Last month, Qaddafi threatened twice to cut off Libyan oil shipments to the United States, a move that shook White House national security adviser Zbigniew Brzezinski and prompted President Carter to dispatch Undersecretary of State David Newsom to Tripoli.

Newsom's visit, the first senior-level official contact with Washington in years, focused attention in both capitals on America's oil imports from this sprawling North African state, as well as on Qaddafi's radical image.

The radical image and Qaddafi's persistent and virulent anti-U.S. rhetoric have done little to cool business relationship between the two countries, however, particularly for American oil companies operating here. There is a clear reason for this - profit.

The American oil companies operating in Libya - officially known as the Popular Socialist Libyan Arab State of the Masses - include Exxon, Mobil, Occidental, Continental and Marathon. They earn 45 to 50 cents a barrel on their Libyan production - more than the companies get from operations in nearly every other OPEC state, and in a few instances, twice as much.

"The door is still open here," said one Western executive here assessing the relations between the Libyan and the American multinational oil companies.

Sitting in his office in former King Idris' palace, Staff Maj. Abdul Salaam Jalloud, Qaddafi's top lieutenant and Libya's de facto prime minister, agreed.

"The American companies have their stability here, and they have more reasons to stay here," Jalloud said.

Asked about the divergence between Qaddafi's rhetoric and the role of the American-dominated oil industry here, Jalloud said, "We solved our problems" by nationalizing the oil and gaining control over prices.

Reluctant initially to join the Organization of Petroleum Exporting Countries, in 1971 Libya ironically became the first Middle East producer to force the oil companies to renegotiate their concession arrangements in favor of the host country - long before others acted.

Reflecting on the U.S.-Libyan relationship during last month's OPEC meeting in Geneva, Libyan Oil Minister Ezzedin Mabruk said Libya now has a "cordial and profitable arrangement for both parties."

At the Libyan Arab Foreign Bank, Mohammed Ilyas offered another explanation.

"There are many reasons why the profits are higher for the oil companies," he said, citing lower production costs here and the accessibility to U.S. and European markets, which means cheaper transportation costs. On the symbiotic relationship, Ilyas said simply, "Well...besides, we need the companies and rely on them."

In recent years the Libyan national bank has handled more than $10 billion in letters of credit from U.S. banks to finance oil purchases from Libya - now amounting to more than 10 percent of U.S. total imports.

"We have an excellent relationship with U.S. banks," Ilyas said, ticking off a list running from California's Bank of America to New York's Chase Manhattan.

Ilyas gave a final rationale on why the companies have good relations here: "It is not a competitive relationship between OPEC and the oil companies; face it, we raise prices and they benefit from our price increases too."

The benefits from the American oil connection that transformed Libya from the world's poorest nation - as it was known in the 1950s - into one of its wealthiest have not been lost on Qaddafi.

"We trust in American technology, especially in the oil field," Jalloud said unabashedly.

Because of its American oil connection, Libya has one of the most balanced oil economies in OPEC, the result of a diverse spread of American companies operating here as compared to the concentrated presence of companies specializing in a few sectors in countries such as Saudi Arabia or Kuwait.

Oil is not the only American tie to the Libyan economy.

This year American enterprises such as Boeing, General Electric, and various agricultural companies will do business worth more than $400 million in Libya - compared to $5.5 billion the U.S. will pay out to Tripoli for oil.

"You can never separate economics from politics," Jalloud said, adding that if political relations improved, American exports would quickly double. Meanwhile, according to one European diplomat, "Americans, despite the problems, are still getting contracts here that Libya has absolutely no need to go to the U.S. for."

Another top official held out even larger prospects: "We have a $30 billion, five-year plan, and American businesses could be more than assured of their share," he said.

There is little question that an untapped demand for American consumer and capital goods exists in Libya.

Counterfeit Levis are sold in Tripoli's market and young Libyans walking along Qaddafi's Green Square are seen wearing T-shirts marked "Skateboarding - California" or "Arizona is for Lovers."

Meanwhile, Qaddafi sends nearly 5,000 college students to the United States to study each year, most of whom are on government scholarships. Far fewer are sent to Europe and almost none to the Eastern bloc countries. It is no surprise that English is the mandatory language in all secondary schools.

"Put yourself in the colonel's shoes," argued one American businessman here. "You want to buy a steel mill and an airplane, and that means Boeing, GE and the works...Western technology. He doesn't want to buy Russian bloc stuff or overpriced European goods."

The close relationship with American business has brought more than 2,500 Americans into the country, primarily to work with the oil industry or on agricultural development, a key government priority. They live easily among other foreigners and Libyans and their children attend American-style schools supported by the oil companies.

While the number of private Americans has been growing, the U.S. official representation has been shrunk by strained diplomatic relations. Fewer than a dozen diplomats headed by a charge d'affairs pad around in the dusty, cobweb-filled U.S. embassy - an office building with many corridors closed off.

The strained relations are often a target of the businessmen, who are quick to note the financial gain to be made from Libya's oil millions. Many businessmen are believed to be quietly urging the administration in Washington to adopt a more forthcoming stand toward Qaddafi.

Some U.S. executives here are more openly critical of Washington's policies.

"There are always two or three orgres in American policy, and Qaddafi is one of them now," said one businessman.

Ahmed Shahati, Qaddafi's press spokesman, blames Libya's poor image in the United States on "misreporting and the Zionist lobby."

Libya and its friends have tried to do something about this, although not with much success.

In one recent effort to improve relations, Qaddafi personally sent Shahati to the United States earlier this year in a tour that ended up as a public relations gaff when the Libyan delegation went to visit President Carter's brother Billy in Plains, Ga. Billy Carter's subsequent intemperate remarks about Jews and Arabs raised a storm of protest and brought a personal remonstrance from the president, bearing out the counsel of Libya's corporate friends not to make the Plains trip.

"Of course Billy Carter is our friend," Shahati said. "My impression is that he is a sincere man and we respect him. We have spoken with him recently, and he thanked me because I suggested he stop drinking, and because I had encouraged him to live as a spiritual and religious man."

Suggestions that the Libyans had sought to win access and concessions from the Carter administration through the president's brother are brushed aside here.

"In exchange for a visit here, we paid a visit there. We also met with his wife and son and mother," Shahati said.

Shahati called his trip a success. "I got a very positive impression from the business community," he said.

Shahati's office is now trying to set up Libyan-American friendship societies in Louisiana, Georgia, Wyoming and Idaho, with memberships drawing largely on companies interested in doing business here.

The Libyans also have funded a chair in Arab studies at Georgetown University for $750,000 and last month helped fund a university seminar at Ann Arbor, Mich., on Arab and Islamic studies.

Still, while the multi-billion-dollar American oil trade has increasingly tied the U.S. and Libyan economies together, political tides in both capitals have moved Tripoli and Washington farther apart.

Newsom's visit, which one U.S. diplomat said "did a lot to clear the air," could lead to a new level of understanding, and possibly accommodation. At the least, it capped a year of high-level diplomatic feelers to the United States from Qaddafi - the most recent of which was passed on by Yugoslavia's President Tito - for dialogue.

Jalloud said, "We told them it is time for them to reassess their position on Libya, that it is time to stop threatening."

Newsom, returning to the United States from Libya, said, "We have an interest in good relations with Libya, but explained our differences on terrorism, support for liberation movements and the Middle East settlement."

A month has passed since Newsom's mission to Tripoli, and there are no signs of a U.S. policy reassessment.

Meanwhile, here in Tripoli, a Western diplomat, grasping for a description of how Washington has dealt with Qaddafi, said: "It's as though it's a chip, a chip to be played and sacrificed for the larger interests," adding almost as an afterthought, "But even the best relations here wouldn't mean a more moderate Libya." CAPTION: Picture 1, COL. MUAMMAR QADDAFI...receptive to U.S. technology; Picture 2, About 97 percent of Libya's 2.7 million population is Moslem, most living in cities and towns along the country's 1,000 miles of Mediterranean coastline. By J. P. Smith - The Washington Post; Picture 3, Most of Libya's 679,358 square miles is barren desert or rock-strewn land. Marathon Oil Company.; Picture 4, Libyan Oil Production and Export Revenue, By Dave Cook - The Washington Post; Picture 5, Libya sells 2 million barrels of oil a day; 40 percent of it to the United States. The Washington Post