When guerrilla leader Robert Mugabe becomes prime minister of an independent Zimbabwe shortly, he will be thrust reluctantly into the center of the fight for the final, most important prize in the battle for black rule in Africa.

With the end of white control in Rhodesia African nationalists will now focus their campaign on white-ruled South Africa. Only the supremely optimistic can envisage the arrival of black-majority rule in the industrial giant of the continent without a guerrilla war involving outside assistance.

Mugabe and President Samora Machel of Mozambique are among the few African leaders to have gained power through this route. They are therefore well-placed in African eyes to head an offensive against neighboring South Africa, possibly replacing the familiar faces of Tanzania's Julius Nyerere and Zambia's Kenneth Kaunda in leading the cause of majority rule.

Zimbabwe is the product, in effect, of the front line states neighboring Rhodesia since they harbored and aided thousands of guerrillas who fought for independence. Now Zimbabwe itselfwill become a front-line state against South Africa.

Mugabe is bound to have misgivings about taking on the fight, which promises to be lengthy, whether peaceful or violent, as his economy is closely tied to South Africa. Tackling the massive problems of a country divided and devastated by seven years of war undoubtedly will be Mugabe's concern.

Thus, at least for the immediate future, the emotional demands of Africa will probably take a back seat to the practical needs of Zimbabwe.

The likelihood is that Zimbabwe and South Africa will learn to live with each other in a similiar fashion to that worked out by Mozambique and South Africa.

In fact, Maputo has certain advantages in its relationship to Pretoria that Salisbury will not have. Mozambique is a source of labor and provides port facilities useful to South Africa. In contrast, land-locked Rhodesia currently relies on South African ports and its more developed economy is bound to provide competition with South Africa as it seeks markets to the north.

Even though Mugabe has gained political power, the white minority still controls the economy. Many would doubtless flee south, with disastrous effects on the economy, if Zimbabwe began to sponsor a guerrilla war against South Africa.

At least until he has achieved stability, Mugabe is likely to adopt a policy of publicly condemning South Africa for its racism but privately maintaining trade ties and open borders.

South Africa is used to such delicate relations with African countries. Zambia's Kaunda repeatedly attacks South Africa orally while relying on it for vital supplies. Just this week his country became the first independent black African nation to open direct air service to Johannesburg.

Zimbabwe will prudently consider how far it can go in anti-South African actions without incurring difficulties. "Mugabe will be careful because he has to be careful," a Western diplomat said.

To maintain his nationalist standing,the new prime minister is expected to allow the establishment of offices by two guerrilla organizations opposed to South Africa, the African National Congress and the Pan African Congress. He has frequently said, however, that he will not allow them to use Zimbabwen soil to launch attacks on South Africa.

One of the first breaks Mugabe is likely to make with South Africa will be to cut off sports competition as other black African countries have done Since Rhodesia was a pariah in the international community during its illegal independence, South Africa provided practically the only avenue of international competition.

Namibia, which is controlled by South Africa despite United Nations demands for its independence, will probably be the initial place where the impact of the guerrilla's electoral victory will be felt. Other than South Africa, it is the only remaining area of white rule south of the Sahara.

Negotiations with the United Nations over independence have been moving tortuousy for years while South Africa has sought to find moderate blacks to put in power instead of the Marxist-oriented Southwest African People's Organization, which has carried on a low-key guerrillawar.

The initial message from Namibia is that South Africa will stiffen its stance as a result of the election outcome in Rhodesia.

Gerrit Viljoen, the South African administrator of Namibia, said the Rhodesian result showed that it was impossible to have free and fair elections when guerrilla forces, although confinedto assembly camps, are not disarmed. One of the contentious issues still to be solved in the Namibian negotiations is the disposition of SWAPO guerrillas during the election campaign.

In the long run, however, South Africa seems likely to cut its losses and accept internationally supervised elections, even if it does result in a SWAPO victory. The alternative is the prospect of an escalation in guerrilla warfare, more damage to the government's credibility with South African blacks, and, eventually, limited U.N.sanctions.

The victory of the "radicals" in Rhodesia also is a sharp setback to South Africa's design for a constellation of southern African states linked to Pretoria economically. A "moderate" Zimbabwe was to play a key role in such a scheme.

The lesson for Pretoria in the Rhodesian election is that it "should pay more attention towhat leftist nationalist leaders say," a South African source said. He added that Bishop Abel Muzorewa, the man South Africa had pushed for years as a moderate alternative to the Marxist-oriented guerrilla parties was "white-tainted."

South Africa lavished millions of dollars on Muzorewa's disastrous campaign. The result in last week's vote was that he ended up with more South African-provided helicopters, four, than seats in the parliament, three.

One of South Africa's greatest concerns is over the possibility of an increase in Soviet influence in southern Africa, and therefore it will closely watch the development of Zimbabwe's relations with the Communist Bloc. Mugabe has had cool relations with the Soviet Union because he received most of his military assistance from China, but the Soviets can be expected to try to woo him.

Although Mugabe has Marxist leanings, the advent of an independent Zimbabwe will open the way for the West to influence the future of the country through aid and trade opportunities.

Both Mugabe and his coalition partner, Joshua Nkomo, apparently recognize that the West offers more fertile ground than the East in these areas. Britain has promised aid to the new nation and the United States and the Common Market ar expected to join in as well. "Zimbabwe," a Western diplomat said, "is bound to be the darling of the international community" as long as it doesn't undertake wholesale seizures of property or move precipitously towardthe East Bloc.

The prospect of Western economic links and pressure from Pretoria, means that Zimbabwe will not be quickly followed by an independent Azania, the African name for a black-ruled South Africa.