After a decade of periodic tensions and repeated setbacks in their relations. the United States and Sudan appear to be on the verge of establishing close ties.

If a breakthrough occurs, it will be due partly to the persistent efforts of Sudanese President Jaafar Nimeri and partly to shifts within big-power and Arab rivalries in northeastern Africa.

A broad array of Western nations and conservative Arab oil powers led by Saudi Arabia and Kuwait have come to the economic and diplomatic rescue of the Nimeri government which had depended heavily on Moscow for arms and aid until a few years ago.

Today, the Soviet Union and its new-found Arab ally, Libya, are regarded here as the country's prime enemies. The new backbone of Nimeri's foreign policy is an American-blessed triangular partnership among Egypt, Saudi Arabia and Sudan.

The overt and concrete support of the United States, which was previously lacking seems now to be in the making.

There is a steady stream of American businessmen to the Nile River capital these day. The U.S. Agency for International Development is cranking up a new, $10 million to $20 million economic assistance program and Washington just recently approved the sale of arms to this country.

"Relations between us and Sudan are developing in a very satisfactory direction and are now very good," says U.S. Ambassador William D. Brewer. "We are working to develop a very meaningful program here."

It has been a long, hard, uphill struggle for those favoring closer Sudanese-American relations to break a diplomatic logjam dating back to the 1967 Arab-Israeli war, when Sudan abruptly severed its ties with the United States.

Then, having taken the initiative among Arab states to renew relations with Washington in July 1972, Nimeri saw his overture spoiled by the assassination of U.S. Ambassador Cleo Noel and his top aide, George Curtis Moore here in March 1973. A heavy pail immediately fell over relations between the two countries, made even worse by Nimeri's decision under Arab pressure to release the Palestinian terrorists responsible for the deed.

In fact, Washington recalled Ambassador Brewer in June 1974 for six months in protest. Strong lobbying by the State Department's irate foreign service officers prevented any significant thaw in the prevailing coolness in relations until last year.

Now, however, things are visibly changing - and at a crucial moment in the life of the Sudan. Nimeri has veered sharply toward the West and the conservative Arab oil states in search of both economic and military assistance to bolster his hand against Libya and Ethiopia, the two neighboring nations he is now convinced are conspiring with Soviet blessings, to overthrow him.

The 47-year-old general is still recovering from the trauma of the nearly successful Libyan-sponsored coup attempt against him last July. That event has apparently removed any lingering doubts he might have had about the need to beef up his security apparatus and also to switch his source of military supplies from the Soviet Union to the West.

Reports circulating here say that Nimeri is considering the purchase of up to half a billion dollars worth of Western arms in the next few years, with the cost to be borne primarily by Saudi Arabia.

In mid-November. the outgoing Ford administration ruled that Sudan was now eligible to buy American military equipment. Pentagon sources said at the time that Nimeri's first request would probably be for communications equipment and sensors for monitoring anti-government activities within this sprawling, million-square-mile nation, the largest in Africa.

Actually, private American companies are already working here to improve the country's communications system. Northrop Page built the gorund station to tie Sudan into the international satellite communications system, and another American firm, Harris Corp. of Cleveland, has an $18 million contract to provide telephone, telex and television links between Khartoum and the country's 13 provincial capitals.

According to unconfirmed reports here, the United States proved its potential value to Nimeri in the security field when it intercepted a radio message among the conspirators involved in the July coup attempt and warned the president of the trouble that lay ahead shortly before his plane landed at Khartoum airport. He was returning from a visit to the United States and France.

Since the November ruling by Ford, a number of Sudanese have reportedly gone to the United States for security training, although there seems to have been no firm decision taken yet on any specific arms sales. U.S. embassy officials here are extremely reluctant to discuss the whole arms issue, however, apparently because of uncertainty over the new Carter administration's policy toward Sudan and arms sales in general.

Sudanese officials have long expressed to American journalists their desire for a closer relationship with the United States, and their frustrations over the slow progress in American-Sudanese ties. Even now that a breakthrough has apparently come, it is unlikely the United states will have a full-scale AID program before the 1979 fiscal year because of the cumbersome bureaucratic procedures involved in launching it.

AID Director Frederick Machmer said he is planning projects in the areas of road building, agriculture extension, manpower development and health. But all await approval from Washington, and the final shape of the program is still uncertain. Thus, it seems likely that U.S. military assistance will precede any economic aid to the country.

The big spur to improve American-Sudanese relations came last June, when President Nimeri made a 20-day visit to the United States.Significantly, his trip was made after first consulting with King Khalid of Saudi Arabia and President Anwar Sadat of Egypt, whose governments are believed to have encouraged the whole reconciliation process between Khartoum and Washington.

During his stay, Nimeri met not only with President Ford, but with a wide range of Pentagon, congressional, World Bank and private business leaders. He reportedly made an extremely effective sales pitch on behalf of Sudan, stressing its strategic importance and its enormous economic potential.

As a result of his personal diplomacy and also of the growing attraction of Sudan as a long-term investment market, American firms, particularily agribusiness concerns, are showing considerable interest.

Nimeri has established a special inter-ministerial committee to foster Sudanes-American relations, especially the expansion of the technical and economic cooperation. It is headed by Mansour Khalid, the former foreign minister and now special adviser to the President on foreign policy matters.

One of the main aims of the special committee is reportedly to help American investors overcome the voluminous government red tape and execute their projects with a minimum of delay. Dealing with the local bureaucracy is still a major obstacle for investors.

But with Sudan embarking on a $6.5 billion six-year development plan, and the Arab nations planning to invest $5.7 billion over the next 10 years, business prospects are regarded as excellent by Western economists and businessmen here.

Among American companies already working in Sudan or scouting investments here are Allis Chalmers Corp., Chevron Corp. and American Pacific International INc. which are exploring for oil in the Red Sea and central Sudan; two Honolulu-based agribusinesses. Alexander and Baldwin, Inc., and Hawaiian Agronomics, plus King Ranch Inc. Tenneco. Inc. Bechtel-McLaughlin, Inc. Mack Truck Inc. Ford, Hilton Hotels Corp. whose new Nile Hotel opens here in March, Sheraton Corp. of America and Holiday Inn, Inc. and Northrop Page and Harris in the communications field.