A request by Sudan for substantial American military assistance is becoming a critical test of the Carter administration's policy on the sale of arms.

It raises directly the issue of the American response to the current Soviet offensive to expand its influence throughout the African continent. Washington must decide where it stands in the worsening cold war between moderate pro-Western and Marxist pro-Soviet regimes in Africa, and whether it intends to assists actively those countries seeking to lessen their dependence on the Soviet Union.

The sale of U.S. arms of Sudan would seem certain to heighten the sense of rivalry and confrontation between the United States and the Soviet Union throughout Africa. It would serve to internationalize further the various conflicts besetting the Horn of Africa in particular. In addition, it would obviously fly in the face of the Carter administration's professed desire to curb the flow of American arms to The Third World.

Yet, if Washington is not responsive to countries that are turning to the United States for military assistance, the immediate effect could well be to undermine the continent's moderate pro-Western states and to convince other countries now dependent on Soviet arms, Sudas Somalia, that they have no viable alternative.

In fact, the Somali government had pretty much come to this conclusion, believing that the new American administration has neither the political will nor the congressional backing to help it lessen Somali dependence on the Soviet Union.

The issue of the American arms policy towards Africa involves not only the feelings and decisions of such countries as the Sudan and Somali, but also Washington's relations with its key ally in the Arab world, Saudi Arabia. With help from other conservative, oil-wealthy Arab states Sudas Kuwait, Saudi Arabia has become perhaps the main countervalling political force to the Communist world in northeastern Africa.

While the Saudis have the oil and dollar power to help Sudan and Somalia lessen their dependence on the Soviet Union, they do not have the weapons and technical expertise. For these, they are looking to the West particularly the United States.

The interplay of Saudi, American and Soviet policies concerning arms is very much evident these days here in Sudan.

Saudi Arabia has promised this country $250 million to help get it off the Soviet military hook and to procure arms in the West, according to diplomatic reports here. President Jaafar Nimeri has already indicated a clear preference for American arms and political backing, undoubtedly with Saudi blessings and encouragement, and is awaiting Washington's reply with growing impatience and doubts.

So far, he has been able to purchase only six C-130 transport planes from the United States. But he would like to purchase F-5E jet fighters and other American arms as well to replace the outmodel or simply unserviceable Soviet ones that make up the bulk of Sudan's moderate-size arsenal.

Nimeri's relations with Moscow had been cooling for some time, but his concern about the state of Sudanese arms has only recently become a major one. The Soviet decision this spring to move into Ethiopia and take over the U.S. role as that country's main arms supplier jolted Sudan into cutting all its military ties with the Soviet Union as a national security measure.

Nimeri has been convinced since the nearly successful coup attempt against him a year ago that Labya and Ethiopia, now both Soviet allies, are conspiring against him and actively aiding his opponents on the left and right. Thus he feels he can no longer trust the Soviets to help him assure the security and stability of his regime.

He has just expelled the 90 Soviet military advisers serving with Sudan's 48,000-man army and also told Moscow to cut the size of its embassy staff by half, a measure taken just as Ethiopia was ordering the United States to do exactly the same thing in Addis Ababa. Meanwhile, the Soviet ambassador here, Felix Fedotov, has been recalled to dignal Moscow's displeasure with the turn ofevents here.

Even before this formal military break with the Soviet Union, however, Nimeri had launched his diplomatic campaign to find arms elswhere and to improve his standing with the West. He visited the United States just a year ago, was on a state visit to France last month and is now in Peking.

Since he has publicly said that he is seeking arms specifically from Britain, France, China and the United States, it seems no secret that this is one of the main purposes of his current Peking visit, particularly since the Chinese have already provided Sudan with a squadron on Mig fighters.

But Sudanese officials do not hide their hope that the United States will become their country's main source of arms supplies, with Britain, China, West Germany and France serving to complement the main American role.

The policy issues; then, seem to boil down to two: Should the Carter administration agree to play this role? And if so, will Congress go along with such decision?

American policy-makers seem to be of two minds. On the one hand, there seems to be a growing sentiment in Washington that the Sudan has enormous potential for becoming one of the worls's new "breakbaskets" and one of Africa's economic giants in the future. Already the conservative, oil-wealthy Arab states are investing hundreds of millions of dollars to expand the untapped agricultural resources of Sudan by harnessing the waters of the White Nile and Blue Nile rivers.

In the long run, a stable and economically prosperous Sudan backed by the technical expertise of the West, could well become a model of development. The political and economic benefits to the United States of helping this to happen seem obvious enough both its African and Arab policies.

On the other hand, providing military assistance to Sudan at this particular point in the political turmoil that prevails in northeastern Africa would seem to carry considerable risk of deeper American involvement in the affairs of this region - just as Ethiopia's decision to end the U.S. military program there has given Washington a golden opportunity to escape such an entanglement.

With Ethiopia in full revolutions and the military government there at deep odds now with Sudan's Nimeri over his backing of Eritrean separatists and other Ethiopian opposition elements, the chances of a direct confrontation between the two neighboring countries seem to be increasing.

Nimeri has stressed that the arms and military assistance he is seeking from the United States are strictly for defensive purposes and to enhance his regime's internal security. Even so, Washington could not reasonably expect to provide defensive arms and remain on the sidelines in the case of a Sudanese-Ethiopia conflict.

One possible solution to this U.S. policy dilemma could lie in a coordinated Western approach toward Sudan's military problem, with the United States, France, Britain and West Germany each providing some of the arms but with no one power obliged to take on the responsibility for overall Sudanese defense.

The political advantages to Sudan of such an approach were made clear during the recent Zaire crisis. When the United States refused to respond to President Mobutu Sese Seko's SOS for military assistance to crush the Angolan-backed rebellion in Shaba Province, he was able to turn to France and Belgium for help because these countries were also giving military assistance to Zaire.

As things turns out, the American refusal to get involved in the Zaire crisis provoked a far African solution to an African problem than anyone expected - with France flying Moroccan troops to Mobutu's rescue. This solution also prevent full-scale East-West confrontation over the Shaba rebellion.

But the lesson of that crisis for Mobutu and the United States seems to be that having more than one Western power involved in providing military needs and requests. Indeed, the overwhelming impression one gets here is that France, Britain and the United States are more fierce competitors for the sale of arms than allies working together for a common cause.