The Reagan administration, determined to fight global terrorism, must still decide what to do about the radical regime in Libya -- a government accused by the United States of underwriting terrorists, which sends troops into neighboring countries and buys billions in arms from Moscow.

But there is another fact about Libya that may get in the way of the administration's principles, and definitley makes for tough foreign policy choices. It is that Libya is the third largest supplier of oil to the United States, providing about 11 percent of U.S. needs. In return for a special type of crude oil used by many refineries on the East Coast, the United States ships some $9 billion a year into the treasury of Libya's radical leader, Col. Muammar Quaddafi. About 2,000 Americans, many of them connected with U.S. oil companies, make their homes there.

Last year, it was Billy Carter's financials connections with Libya and possible influence peddling that caused big headlines.

But this year a new administration is far more concerned with containing Soviet influence around the world and the work of what it sees as Soviet surrogates. The administration is bothered most by the $12 billion stockpile of Soviet arms that Quaddafi has built up and by the successful military intervention of the colonel's forces into the neighboring country of Chad.

The invasion of Chad and the continued presence there of 6,000 to 7,000 Libyan troops -- most of them Moslem mercenaries recruited from other countries -- has angered and frightened a dozen neighboring countries in northern Africa and has revived fears that the mercurial Quadaffi was setting out again to create his vision of a pan-Islamic empire of Saharan states.

The intervention also puts Libyan troops near the border of Sudan, a country friendly to the United States.

What to do about Qadaffi, who also has some 5,00 Soviet, East European and Cuban advisers in his country, is now the subject of intense review within the administration. While there tends to be agreement that Quadaffi himself is in danger -- one senior official describes him as a "mini-imperialist and supporter of terrorism, an old-fashioned tribal leader who feels a mystical air about him and doesn't have much respect for a country's boundaries" -- there is not yet agreement on how to handle him.

The Libyan leader is not viewed as especially vulnerable on his home ground, though there have been reports of a mutiny involving army troops in Tubruk last summer. But any direct move against the colonel would undoubtedly be risky, especially with so many Americans there.

Within the State Department, there appear to be two schools of thought, although, as one official says, "nobody advocates being nice to him."

The department's African specialists, sources say, tend to view Libya as primarily a regional problem. The United States can best solve the problem by backing existing resolutions by many African states against Quaddafi and by encourgining them and the French, with long ties in the region, to get the Libyans to change their ways. In this view, the Africans are closest to the situation and know the intricasies better than does the United States.

A more confrontational view is said to be espoused within State's policy planning staff. This would invlove an attempt to draw the line on Libyan expansionism and stop it in Chad. Otherwise, it is reasoned, Quaddafi's "delusions of grandeur" will drive him further, possibley into Sudan or Algeria.

The harder line also views quaddafi as Moscow's surrogate, sowing the seeds of disruption in a band from Morocco in western Africa through Egypt and across the Red Sea into Saudi Srabia. President Reagan has also talked publicly of Quaddafi being a Soviet surrogate.

Opinions differ about the depth of Libyan-Soviet ties. For example, in one view, the massive stockpile of tanks, planes and guns bought from Moscow -- far beyond the apparent needs of a country of less than 3 million people -- may really be meant as pre-positioned equipment for some future Soviet thrust into the Middle East. But others believe that the arms are more of a reflection of Quaddafi's desire for weapons and the Russian desire for hard Western cash that Libya sepnds for the arms.

Similarily, some skeptics believe that Quaddafi is too much his own man to be exclusively a puppet of Moscow too unpredictable, disorganized and unreliable for Moscow to ever count on in a crunch. The Soviet leadership, some here feel, probably views the Libyan ruler as another religious fanatic not unlike Ayatollah Khomeini.

If the administration eventually chooses to take sterner measures against Quadaffi, then the questions of oil, money and American'n in Libya -- all issues that could generate considerable pressure here at home -- may have to be dealt with. Officials say the special kind of "sweet" crude exported by Libya culd probably be replaced from other markets, but they say it would not be easy and the quality of possible replacement deliveries may not be as good.