The sleepy little town of Cradock, set on the sheep-farming plains of a dry central plateau called the Great Karroo, is hardly the place one would expect to find a flashpoint of the gathering South African racial conflict.

Small-town South Africa is the repository of the country's innermost spirit. In these sleepy villages of a few hundred souls, dotted every 30 or 40 miles across the spacious veldt, the racial order is not for questioning.

City ghettos such as Soweto and Crossroads may burn with the anger of an oppressed race, but here, for generations, the black folk have known their place, and the lowliest white man has been greeted deferentially as "baas" and "master."

Suddenly this has changed. Now it is not only the cities that are caldrons of conflict. Over the past six months unrest has spread to the small towns as well. Scores of unfamiliar names appear among the growing list of South Africa's trouble spots: Kroonstad, Vryburg, Vosloorus, Paarl, Parys, Vergenoeg, Newton and Cradock.

The Karroo village has become the hottest spot in this new platteland, or outback, revolution that is testimony to the spread of political consciousness among the segregated republic's 21-million black African majority.

For 13 months, all black schools in Cradock have been empty as militant students have boycotted classes in rebellion against the white authorities. All the school committees, and a council elected under the apartheid system to run the segregated "location" where the blacks live two miles outside the white town, have resigned under black pressure.

This has brought the system of black administration in Cradock to a standstill. The only representative body left is a residents' association that this once quiescent community established two years ago.

At first the white authorities refused to deal with the association, called Cradora. Government policy is to deal only with black institutions officially established under apartheid.

They tried to crush it by detaining its leaders and subjecting its supporters to a campaign of repression. There have been violent clashes between residents and the police that have left four people dead and several injured.

But instead of crushing Cradora, the repression seems to have increased its support and hardened the resistance of the now tightly cohesive black community.

It has been an illustration of what has been happening in South Africa since widespread racial unrest began last September, with the white-minority government trying to end black dissent by cracking down, further alienating and radicalizing the black communities.

The blacks of Cradock have jolted the town's whites by mounting a boycott of their shops that sent a deputation hurrying to the government for help.

Now the blacks have won a kind of official recognition, if not yet redress of grievances. Some restrictions on their association have been lifted, their leaders have been released from detention, and last month a deputy minister of black affairs, Sam de Beer, received a delegation from Cradora headed by its president, Gladwell Makaula.

Behind Cradock's political awakening lies a bright young teacher named Matthew Goniwe, the son of an illiterate domestic servant and an itinerant firewood merchant. He returned to what was his birthplace two years ago and, in the language of African nationalism, began "conscientizing" its docile black community.

Goniwe, 29, had spent four years in prison in the tribal homeland of Transkei for holding ideas on black emancipation that are regarded as subversive here. He used the time to win a degree in politics in addition to his educational diploma.

When he arrived in Cradock, Goniwe organized a youth association. Then, when the administration increased rents in the little black "location" called Ilingelihle, he formed Cradora.

Immediately the white administration transferred Goniwe to a town 100 miles away, saying that the black school there needed a math teacher.

Goniwe, the only math teacher at his Cradock school, decided this was a ploy to get him out of the way and refused to accept the transfer. He was fired.

Outraged students who had come to regard him as their leader began a boycott of classes in February 1984 to demand his reinstatement. They have not been back since, and their protest has expanded to involve the entire black community of 15,000.

A spiral of racial confrontation followed. The government banned all Cradora meetings. When the students held a meeting of their own last March, police broke it up with tear gas and clubs.

This sent the angry students rampaging through the township, after which the security police detained Goniwe and most of his Cradora committee.

Attitudes in Ilingelihle hardened further, and clashes with the police became more frequent. The students struck back by burning the houses of village council members and other blacks connected with the administration. In January the council members quit rather than take further punishment.

The clashes have been vicious. A white opposition member of Parliament, John Malcomess, has sent 13 sworn affidavits to President Pieter W. Botha alleging misconduct by the police in Ilingelihle, including the killing of a 15-year-old boy.

On Feb. 3 the body of a policeman was found on the banks of the Fish River, which runs through the town. A student leader, Madoda Jacobs, has been charged with murder.

The white authorities "wanted to kill our organization," Goniwe said in a recent interview. "Instead, they hardened the reaction of the people."

"Whenever the police move into the township, that produces the clashes," he explained. "The people have been embittered and they react when the police attack them. They are not afraid anymore. They no longer run away when they see the hippos," armored personnel carriers used by the police.

There is no end to the conflict in sight. After his meeting with the Cradora committee, Deputy Minister de Beer still refused to reinstate Goniwe and another suspended teacher, Fort Calata. So at a meeting two weeks ago, residents decided to continue the boycott of classes for the 1985 school year.

As a teacher, Goniwe says he is troubled by the use of school boycotts as a political weapon, but he says there are few weapons available to voteless blacks.

"We know we will be the first to suffer, but if it helps us win our demands, then let it come," he said.

The government refuses to reinstate Goniwe and there are no schools for blacks other than those run by the state. He cannot find another job in the town, where the whites regard him as a troublemaker. He and his wife, Nyameka, live on her salary as a social worker.

But Goniwe regards the year of conflict in Cradock as one of achievements rather than setbacks.

"There is no doubt that the people of Cradock have a highly developed political awareness as a result of what has happened," he said. "And now at last we are beginning to get some results. It is the only way."