As they had done so many times before, black civil rights marchers locked their arms in unity yesterday and walked through a southern city.

They raised their voices and their signs to protest the suppresion of blacks in South Arica, suppression they had once protested in their own American south. They walked peacefully, some 2,000 strong, for the three miles or so from the state capitol downtown to the Vanderbilt University area where a white South African team played a U.S. tennis team in a Davis Cup match.

All in all, so peaceful was the entire day that Metro police lolled at ease - one was seen sleeping in his car - and escort officers professionally prepared the way for the protestors, buzzing about on motorcycles to block traffic. There were dogs - a stray German shepherd and a leashed English sheep dog out for a walk.

"This is the first major march we've had," said Dick Gregory, the comedian turned activist, "not just in many years but for South Africa." Enough years, it seemed, so that most of today's marchers appeared to be etiher in their 40s or older - the veterans of marchers now almost forgotten - or college-age, perhaps making their first protest.

So it was that older sections of the two-block-long parade sang "We Shall Overcome," and younger participants shouted, "The people united will never be defeated." One group chorused "Hallelu, hallelu, hallelu," and another repeated, same old - ."

And while the NAACP-sponsored rally following the march sang the national anthem and turned to religion ("He's got the whole world in his hands"), those in a protest band led by the Revolutionary Student Brigade turned to rhetoric: "We gonna kick, we gonna shout, we gonna turn this mother out."

In her straw hat and walking shoes, Laura McCray, 69, described herself as a veteran marcher - "Selma and all of Martin Luther King's marches."

"Nok," she said, "black people are identifying with our heritage, and we are not ashamed of it anymore. We have been through the same thing as the black South Africans and we can see the light.

"I'm ready for walking."

"The issues have changed," said Franklin Williams, the organizer of the Coali-tion for Human Rights in South Africa. "The basic civil rights that blacks fought for have extented.The problems now are not access and voting. The problems now are the economy and Africa - Africa is increasingly becoming of concern in America. It's front and center."

It was the first protest for Benjamin Hooks as executive director of the NAACP. He walked hand in hand with his wife, Frances, and on concluding the march declared it all "great." Hooks had earlier called the organization's goal that of producing the biggest civil rights march since the 1960s. But he ended up scaling it down to a hope for 2,000 marchers. He got them, it appeared, and at various locations throughout the city, told today perhaps as many as 3,000 protested the Davis Cup match, South African racial policies and Vanderbilt's decision to host the march.

As they had done the day before, student picketers marched at the entrances to vanderbilt's Memorial Gymnasium and hounded those attending the match with shouts of "racist" "murderers" and other epithets. In the past, civil rights protesters were split at: Yesterday it was a protesters or two doing the splitting.

There were chants of "I don't know but I have heard, Nashville's not Johnnesburg," and signs like "Tennis balls come in colors - why not tennis players?"

An oversized mockup of a South African identity passbook was burned at the gymnasium. In the NAACP march, large blowup new photos of black-white conflict in South Africa were lofted above the crowds.

The throng wasted no time in moving out on its march, and soon "freedom songs" were reverberating off the highrise office building as they moved through the deserted downtown.

They arrived at Centennial Park opposite Vanderbilt University and packed into an amphitheater for speeches by such civil rights leaders as Gregory, Hooks, and Bayard Rustin. Apartheid in South Africa was denounced, and black support in America was announced.

At the same time, at the gymnasium, bullhorns and shouts carried the message of protest to those entering and leaving the gym. "It's my first protest," said a tennis match volunteer worker in his early 20s, as the pickets shouted at him.

"It's interesting," said a fellow volunteer who was the same age.