For nearly two weeks in September 1979, Billy Carter sat around Tripoli waiting -- unsuccessfully -- for an appointment to see Libya's strongman, Col. Muammar Qaddafi, according to diplomatic sources who were in Tripoli at the time.

Qaddafi's refusal to meet with the president's brother in 1979, or in 1978 at the time of his first visit, suggests that the Libyan leadership looked on Billy Carter primarily for his publicity value rather than as a political operative.

For Billy Carter, on the other hand, Libya from the start apparently was looked on as a way to make some money.

Three of his close associates urged him not to go to Libya in 1978 because of the nature of the regime. At least one warned him that he might embarrass his brother. Today, friends of Billy say he disregarded that advice because he felt he needed the money.

For over two years, the Libyans gave Billy Carter nothing but a few gifts and expense money, despite his requests for loans or an oil allotment that could have made him rich.

It was only after he acted as a middleman in setting up a White House meeting for a Libyan diplomat that money started to flow.

The president's brother went to Libya in 1978 and 1979 at the expense of the Libyan equivalent of a foreign ministry.

His trip in 1979 was to attend the 10th anniversary celebration, on Sept. 1, of the coup that brought Qaddafi to power.

At the time, U.S.-Libyan relations were cold. The Justice Department would later say that Billy Carter's presence at the 1979 celebration "was important to Libya" because it created the "appearance of approval by the U.S. of the Libyan revolution" and got media coverage of the celebration.

According to one source, Billy Carter was interviewed by Canadian and French reporters along with Arab journalists. He was later quoted in Kuwaiti magazines as having made anti-Zionist statements.

The White House yesterday released two letters and a cable from William Eagleton Jr., the U.S. charge d'affaires in Tripoli at the time of Billy Carter's 1979 visit.

In a Sept. 12 letter, Eagleton referred to "Billy Carter activities" being "so low profiled that I have not felt it necessary to report anything by telegram."

He noted that the president's brother "has stayed on in Tripoli mainly because of a suggestion that Qaddafi will receive him" -- a suggestion that did not turn out to be true. Eagleton added, however, that Billy Carter "presumably hopes eventually to have some direct or indirect business dealings here, though he said nothing about this and I did not probe."

But Billy Carter had another reason for going to Libya in 1979 and staying around after his wife, son and friends had returned to Georgia.

He was looking for oil -- at least looking to get an allocation for a U.S. refiner of highly profitable Libyan oil on which he could make a commission.

According to personal friends of Billy Carter, he had been given the impression early in 1979 from the Libyans that he could get up to 100,000 barrels a day for the U.S. refiner.

He thought he could get that allocation of Libyan oil for the Charter Oil Co., of Jacksonville, Fla. He obtained letters from that company in August, just before he left the United States, outlining a million-dollar commission for him should he succeed, and detailing just what type of oil Charter wanted.

By the end of September 1979, however, Billy Carter returned to Georgia from Libya without having seen Qaddafi and without an oil allocation.

His publicized friendship with the Libyans, despite heavy criticism in his own country, had not been rewarded with any money.

Two months later, the situation began to change.

At the request of national security affairs adviser Zbigniew Brzezinski, Billy Carter arranged for the new Libyan charge d'affaires in Washington, Ali Houderi, to meet Brzeznski at the White House. Billy Carter sat in on the Nov. 27 meeting.

Nine days later, Houderi met for 10 minutes with President Carter in an unannounced session. That brief talk was apparently important enough for Houderi to go immediately to Tripoli. He returned to Washington just as quickly and had another session with Brzezinski on Dec. 12.

The details of that session have not been announced.

Meanwhile, however, Billy Carter and his colleague Henry (Randy) Coleman were apparently back in touch with Houderi on their own.

Coleman was invited to return to Libya in December. Just before leaving the United States, he stopped at the Libyan Embassy in Washington and picked up a check from Houderi for $20,000 and dated Dec. 27.

The purpose of Coleman's trip, which lasted into January 1980, has not been disclosed either by Coleman or Billy Carter.

Diplomats and journalists who met Coleman in Tripoli in January said recently he talked of being involved in the Libyan-financed Arab American Dialogue, a people-to-people program that was supposed to meet in Washington in February 1980.

After talking to the U.S. Embassy in Tripoli on Dec. 2, Americans who had participated in the first Arab American Dialogue in 1978 in Tripoli, had suggested the February session be canceled. In mid-January it was, and Coleman returned to the United States.

In March, however, Coleman again went to Libya on a trip paid for by the Libyans. Again, there is not direct information on what he was doing.

But while Coleman was in Libya, Billy Carter on March 30 called the Charter Oil Co. He wanted a telex sent to Coleman in Tripoli from the company saying they would be interested in buying any Libyan oil they could obtain on the same terms they were already getting.

The telex was not a commitment letter, a Charter official said recently, but it did identify Coleman to the Libyans as someone with a relationship to an American refiner.

At the time, Charter along with other American purchasers of Libyan oil -- faced a sharp cutback beginning April 1. Their previous 100,000 barrels a day was cut to 60,000 barrels and a new contract was to run only until Dec. 31, 1980.

Billy Carter told Charter officials on the phone and at a lunch the next day in Jacksonville that he felt he could get them the oil they wanted.

Coleman, however, apparently returned to the United States empty-handed. Charter officials said recently they called him several times in succeeding weeks -- since they needed the oil -- and got no encouragement from him that any new allotment would be forthcoming.

On April 7, however, within a day or so of Coleman's return from Libya, he again stopped by the Libyan Embassy in Washington and picked up a check for $200,000 for Billy Carter.

The check itself, according to those who have seen it, has the word "loan" on it, and Billy Carter has claimed it was part of a promised $500,000 loan.

The money came from a foreign ministry account. In terms of what Libya and other oil-rich Arab countries have spent for public relations, it was not much.

One word from Qaddafi and Billy Carter could have had the oil allotment that would have made him a millionaire. It never came.