For an outcast country ruled by an eccentric Bedouin soldier called "Brother Colonel," it was perhaps natural to turn for help in America to "brother Billy."

Libya, 670,000 square miles of desert in northern Africa, has built much of its "green revolution" on such impatience with the traditional ways of Western-style democracy and with the foreign rules of diplomatic practice.

Col. Muammar Qaddafi, whose "Green Book" interpreting the Koran is the revolution's manual, took over at age 27 from an aging king in a bloodless military coup in 1969. Since then, in unpredictable spurts, he has turned the Western-dominated monarchy into a jamahiriyah. This is his own Arabic neologism meaning literally "massdom" -- run by "people's congresses" instead of a government and based on an uncertain mixture of Islam, Arabism and Qaddafi's homespun ideology of Third World revolution.

Officials of the "People's Liaison Bureau," which has replaced the Foreign Ministry, were in their eyes breaking little new ground, therefore, when they enlisted President Carter's brother in an effort to improve Libya's image among the American people and perhaps the American government. l

Addafi himself ordered Libyan students abroad last September to take over their country's embassies and turn them into "people's bureaus" instead of the chanceries in which Western diplomacy does business. Although in the West the order seemed to be just another antic, it reflected Qaddafi's insistence on doing away with diplomatic conventions regarded in Tripoli as imports from the West.

In a speech at the time marking the 10th anniversary of his takeover in Libya, Qaddafi said: "All the embassies continue to represent government bodies at a time when the government has disappeared in the Libyan jamahiriyah with the establishment of people's power."

In addition, the tradition of family ties and influence is strong across the Middle East. The kingdom of Saudi Arabia, for example, is built on the sharing of power and its perquisites among a large royal family. In neighboring Jordan, King Hussein's brothers naturally have their place in court. Even the Baathist president of Syria, hafez Assad, has entrusted his brother Rifaat with command of special troops assigned to make sure he stays in power.

Against this backdrop, the furor in the United States over Billy Carter's role as a go-between for Libyan diplomats and the White House has attracted slight attention in the Arab world. Even in Egypt, where people from officials to laborers call Qaddafi "the madman," the revelations in Washington have received only sober treatment with modest news agency dispatches in the semiofficial Cairo press.

Disclosure that Qaddafi's emissaries also provided a loan as part of Billy Carters friendship has been greeted by an equally indifferent shrug in a region where the line between bribery and gratitude has always been fuzzy and government officials, business contacts, journalist and other assorted hangers-on are regular recipients of "gifts."

Libya, with oil revenues estimated at $16 billion a year, has been one of the region's most generous givers. Libyan funds finance newspapers, Palestinian guerrilla groups, politicians and Lebanese militias in the Middle East. Outside the region, they have flowed to African groups as disparate as Chadian rebels and Idi Amin's fallen government, and to other groups as far afield as Moslem rebels in the Philippines and the Irish Republican Army.

Qaddafi, whose higher education is limited to the Libyan Military Academy and through autodidactic reading, often has disbursed his riches with the best of revolutionary intentions but little knowledge of what local purposes they frequently serve. His lieutenant, Maj. Abdulsalam Jalloud, was astonished, for example, when he came to Beirut during the 1975-76 Lebanese civil war and discovered the complicated conflict his country was helping finance.

Qaddafi himself has shown signs of being out of touch with reality. On a recent trip to Jordan, he insisted on an open car for "the people" to salute him as he drove in from the airport. Embarrassed Jordanian officials tried unsuccessfully to talk him out of it, but he persevered, got his car and drove into town past empty sidewalks.

In this context, questions being raised in Washington about the propriety of a loan to the president's brother in the United States are unlikely to have come up in discussions in Tripoli. The idea of an inquiring press is unknown in Libya and the "people's congresses" have yet to open any investigations into Qaddafi's conduct in office.

But Libyans and diplomats in Tripoli say there also is another side to Qaddafi's seemingly naive character. It is Bedouin cunning, perhaps, or native intelligence. Whatever its label, they say it has guided Qaddafi through ten years to what is widely agreed to be a firm hold on power through broad popular support among most Libyans except the merchant class, whose property has been taken over.

In addition, oil officials in Tripoli recall the startingly able negotiations conducted by Qaddafi when he took over control of Libyan resources from foreign petroleum companies. Making friends with Billy Carter, therefore, is sure to have looked to Qaddafi like more than a simple response to the Bedouin code where everyone is a brother.