President Jaafar Nimeri, embarked on a controversial policy of Islamization of his country and beset by overwhelming economic problems, is facing opposition from foes in exile and a Libyan-backed armed insurrection at home.

In the south, the Christian and animist minority -- roughly 30 percent of Sudan's 22 million people -- is fighting under the banner of John Garang, an American-educated, ex-colonel. The goal of this soldier, who holds a PhD in economics from Iowa State University, is not to secede from the Moslem north but to overthrow Nimeri.

The two-year-old rebellion in the south is proving to be a real threat to Nimeri. Since Christmas the rebels, estimated to number 15,000 men, have inflicted stinging defeats on Nimeri's troops. Fighting without apparent motivation, the Army in the south has discovered a foe often better equipped, especially with vital communications gear, than it is.

Meanwhile, Sudan's divided opposition in exile is working desperately to settle its differences before its ambitious plans for a return to parliamentary democracy are preempted by a military coup against Nimeri.

Politicians interviewed in London, the unofficial opposition headquarters, are aware that their failure to unite has discredited them with many Sudanese.

"I think we are running out of time," former foreign minister Mansour Khalid said. "If there is a coup today we would be completely irrelevant."

Such pessimism reflects a general view among many Sudanese abroad and in Sudan that the Army remains the country's only organized force capable of toppling Nimeri.

The southerners' fury against Nimeri stems, in part, from his refusal to locate a new refinery in the south, where the U.S. company, Chevron, discovered a major oilfield.

Traditionally resentful of economic and political domination by the north, the southerners argued that they once again were being left with the development crumbs.

Nimeri further enraged the south when he decreed in 1983 that sharia, or Islamic law, should apply to all Sudanese, Moslem and non-Moslem alike.

Many northern Moslems were shocked when Nimeri invoked the sharia, which punishes theft with amputation, but when non-Moslem southerners were among the first victims, the president was seen as needlessly alienating the south.

Sudan's principal allies -- Egypt, the United States and Saudi Arabia -- all privately opposed sharia, but were powerless to dissuade Nimeri from carrying out the change, which they felt could only endanger his government and their larger strategic interests.

The decision to impose Islamic law gave Garang, a Christian, and his movement an emotional cause.

Nimeri, who has relied on massive doses of western aid, now faces yet another problem in the form of a freeze in economic assistance from the United States and cuts by other western nations because of Sudan's worsening financial crisis.

As Nimeri's problems deepen, representatives of the three main traditional political parties say that they finally are on the verge of signing a "national charter."

"It's proving more difficult to find agreement among northerners," who head the traditional parties, Communist Party representative Ezzedin Ali Amer said, than it's likely to be between northerners and Garang's movement.

He acknowledged that his weakened party, once the strongest communist organization in Africa, still harbored "genuine doubts" about its would-be partners in the Umma and Democratic Unionist parties.

Nor are those conservative parties uncritical of the Communists, who helped Nimeri seize power in 1969. At best, the conservatives prefer to have the Communists inside a post-Nimeri government just to keep tabs on them.

Additionally, the Democratic Unionists are said to have unresolved leadership problems as a result of the death of Sharif Hussein Hindi, a major opposition figure, three years ago in exile.

"The opposition seem to have their feet well off the ground," a western diplomat said. That view apparently is shared by Garang. Last summer he did not even acknowledge receipt of an earlier northern opposition charter for proposed cooperation when it was conveyed to him in Ethiopia.

He apparently felt that northern politicians have neither given sufficient assurances to his movement about future relations nor shown any willingness to put teeth into their opposition to Nimeri.

Rightly or wrongly, according to opposition sources in London, Garang feels that the northern politicians are doing nothing and, in one man's words, "want to ride the wave" created by his troops' growing string of military successes against the Sudanese Army.

"Garang is not asking the northerners to take up arms in Khartoum," one source said, "but he is asking for civil disobedience and that leading politicians in Sudan cut their ties with the regime."

"A lot of northerners are ready to cheer Garang," a western diplomat said, "but they are not prepared to die for him."

Especially galling to southerners were a Democratic Unionist leader's membership in the Politburo of the ruling Sudanese Socialist Union and unofficial contacts between Nimeri and Umma Party chief Sadiq Mahdi.

The northerners reportedly also failed to deal with specific questions closest to southerners' hearts -- the end of Islamic law, not just for their Christian and animist followers but for all Sudanese; renewed constitutional guarantees that the south, carved into three provinces by Nimeri despite a promise to the contrary, would again be a single unit, and a multiparty system after Nimeri.

The political parties underscored their ineffectiveness in the eyes of many Sudanese last month when they failed to follow the lead of 12 unions -- representing doctors, lawyers, students, engineers and other groups -- in condemning the hanging of Islamic reformer Mahmoud Mohamed Taha on heresy charges.

Nonetheless, contacts between Garang and northerners has, in one Democratic Unionist politician's words, "proved a mutual education." The opening of a front by Garang near the Kenyan border has encouraged speculation that he is wary of his ties with Marxist Ethiopia and Libya and would like to improve relations with moderate, prowestern Kenya.

That would be welcome to conservative northerners worried by Garang's proclaimed socialist manifesto as well as his choice of allies. They are convinced that Garang recognizes that the aid so badly needed to right Sudanese finances can come only from the coffers of the West, the Arab world and international institutions.

Northerners such as former foreign minister Khalil are working to recruit Sudanese to plan the rehabilitation of their country after the Nimeri era. Despite this improved mood of mutual understanding, however, neither southern nor northern opposition leaders appear to have any clear idea of how they would force Nimeri out. Garang is not thought likely to carry his fight to the Arabized north.

The Communists speak vaguely of "a national uprising, a popular strike, an insurrection." They fondly recall that in 1964 a plot hatched at the University of Khartoum faculty club forced field marshal Abboud to resign in favor of civilian rule by political parties. But that was before Nimeri, in one opposition representative's phrase, "went through all our ranks like a knife through butter," buying off and co-opting aspiring politicians.

The university was closed indefinitely Sunday because of violent clashes between supporters of Nimeri and various opposition factions, Agence France-Presse reported Monday.

At best those politicians wedded to a return to civilian rule are convinced that even a successful military coup would be forced to hand over power in orderly fashion to the parties. But when pressed, the best argument marshaled in favor of such thinking is that the military now know that it is incapable of unraveling Sudan's multiple problems with simple barracks solutions. If Nimeri finally does unite the opposition, he will have rendered a service to Sudan, in the eyes of these politicians.