Pretoria gets the upper hand. THE struggle between the white-controlled government of South Africa and its radical black foes unfolded on at least five fronts last week. There were battles in the schools, the workplace, the courts, and the economy -- as well as the more familiar armed showdowns.

The multi-dimensional nature of the struggle in South Africa between the white-controlled state and its radical black foes has been etched into contemporary history by last week's events. The struggle unfolded on at least five different terrains: educational, military, industrial, economic, and legal. The state appeared, for the most part, to have gained the initiative -- although the campaign is far from over.

On the educational front, the government chose the start of the new term on July 14 for a showdown with young black activists who have used school premises to mobilize young blacks for the fight for majority rule in South Africa. It laid down a series of regulations under the state of emergency. These are designed to isolate schools from the political ferment around them.

The most important of these made it compulsory for all returning students to re-register, for all students to carry identity tags, and for entry into and exit from schools to be controlled by specially trained security guards.

The Department of Education and Training, which is responsible for black education outside South Africa's 10 ``black homelands,'' claimed victory. It reported that an average 8 out of 10 pupils had returned to school and that they had accepted that the new rules were for their own safety. But the department's figures included primary school enrolment and to that extent masked the situation in the 300-odd secondary schools under its control. There are 1.4 million primary school pupils to about 300,000 secondary school students, making a ratio of more than five to one.

Most black observers counseled caution in interpreting the 80 percent return reported by the department. The issue was not yet settled, as evidenced by the official admission that there were boycotts and resistance to registration at a third of the 62 black secondary schools in the Johannesburg educational circuit.

On the military level, South African security forces reported a major success against armed guerrillas of the outlawed African National Congress July 10 and 11. In the space of 24 hours, the security forces intercepted two guerrilla units, killing six near South Africa's northern-western border with Botswana, and four near King William's Town in the eastern part of the Cape. Police casualities were minimal; only one policeman was wounded.

The security force success to some extent neutralized the spat of attacks by underground bombers against white-administered towns and cities. But an important rider has to be added: While the bombs did not need verification -- the havoc they wreaked was there for all to see -- the killing of ANC fighters could not be established independently.

White morale was further boosted with the unveiling in Pretoria of a secretly developed adaptation of South Africa's aging fleet of Mirage F3 fighter planes. Known as the Cheetah, the new plane is the work of the state-sponsored arms corporation. It is said to be more than a match for the Soviet MiG-23 deployed in neighboring Angola.

On the industrial level, the newly-formed Congress of South African Trade Unions -- the largest federation of trade unions in South African history -- challenged the white-dominated state. Cosatu, as the trade union congress is known, called on workers to embark on a ``day of action'' on July 14 in protest against the detention of trade union leaders. Of the 245 trade union leaders and officials known to be in detention, over 80 percent are from Cosatu.

But response to the call was generally meager. Two regions, northern Natal and the western Cape, opted out even before the start of scheduled industrial strikes. In South Africa's key industrial area, known as the PWV, more than three-quarters of the black work force turned out for work in factories organized by Cosatu. In factories not yet penetrated by Cosatu -- or under the control of rival unions -- turnout was even higher. There were few reports of in-plant go-slow strikes or sit-ins.

But the stay-away in the eastern Cape city of Port Elizabeth was virtually total. The eastern Cape is the area where the outlawed ANC has the deepest roots.

Different reasons have been offered for the failure of the Cosatu day of action. At the simplest level, Cosatu officials probably underestimated the extent to which their lines of communication with rank-and-file workers had been disrupted. They almost certainly allowed themselves insufficient time to organize for the protest. Once the decision was taken, they had less than four days to organize a nationwide strike. Two of those days fell over the weekend, when workers were at home.

A related reason for the setback may be that Cosatu shifted too quickly from the factory floor to the political arena. Perhaps it made the tactical mistake of trying to fight a battle on two fronts at once. To avoid this error, union leaders of the old Federation of South African Trade Unions -- from which Cosatu emerged in part -- used to caution against moving too quickly into the political field.

Thus Joe Foster, General Secretary of the now defunct Federation of South African Trade Unions, warned in 1981: ``You can't fight the state and the employers at the same time.... Who is the enemy? The bosses are the enemy. These are the people one should actually direct attention to.'' In defiance of this warning, Cosatu declared war on both the state and the bosses by proclaiming that employers were co-responsible with the state for the detention of trade union leaders.

Battle was joined on another issue -- the rent boycott by black township residents. Last week saw several black town councils attempt to force householders to pay rents by threatening to evict them. A critical contest of will is unfolding in Soweto, largest of South Africa's black townships.

The deadline set by the Soweto council for residents to pay arrears in rent has come and gone. Notices are being served, giving rent defaulters seven days to pay or face eviction. The rent boycott began in June to support demands for a general lowering of rents, the abolition of rents for pensioners, and the dissolution of the Soweto Council, which black radicals call a ``puppet body.'' Two-thirds of Soweto's 75,000 householders responded to the boycott call, reducing the council's revenue from rents from 7.5 million to 2 million rands, the town clerk of the Soweto Council, Nico Malan, said in an interview.

The Soweto Council's campaign has presented many householders with an acute dilemma. If they refuse to pay rent, they risk losing their houses in a society where thousands of people are homeless. (There are 22,000 families on the official waiting list in Soweto.) If they pay up, they risk losing their lives in a nocturnal petrol bomb attack by ``comrades,'' young militants who punish those they deem to be collaborators with the white-controlled government.

On the legal front, antigovernment forces have scored some successes. The courts ordered the release of two people detained under emergency regulations.

And in a more recent case, the full bench of the Natal Supreme Court ruled that five of the six definitions of a ``subversive'' statement in the emergency regulations were null and void. They were too vague to be lawful, the judges found. These definitions were major restraints on political leaders' comments about the state of emergency -- and even on reporting on it.

This report is filed under South Africa's emergency regulations, which prohibit naming people who have been detained, reporting security force actions unless officially authorized, and relaying information deemed subsversive.