In 1979, the American Civil Liberties Union reopened the Brown suit, asserting that the existence of 13 racially segregated schools on either side of Topeka Boulevard violated the 1954 High Court ruling. Signing on to the suit was Linda Brown Thompson, who was 11 when her father and other black parents brought the first Brown suit.

After years of legal maneuvering, in 1993 a Federal court agreed with the A.C.L.U. Now the Topeka district is proposing to close some of the segregated schools, bus more of its 15,000 students across neighborhood lines and create magnet schools, all in the name of integration.

But while several polls have shown that people support desegregation efforts nationally, they tend to fight it locally. Topeka is no exception. The school superintendent, Jeffrey W. Weaver, says he has received anonymous letters and calls with racial slurs from whites and blacks opposing the proposed plan, which was unveiled earlier this school year. He says the attitude among parents whose children will likely be affected by closings and busing is, "Why me?"

This was not the vision of Oliver L. Brown, a minister, or the 12 other parents who went to court in 1951 in an effort to end the city's system of segregating elementary school students by race. They had long recognized that separate was not equal, that the all-black schools their children attended were educationally inferior to the all-white schools down the road. They reasoned then, as research has now shown, that if black children, especially those living in poverty, were sent to well-financed, solidly middle-class schools, they were more likely to adopt middle-class values and get a better education.

"It was unrealistic to expect that we could overcome all these entrenched problems, even in 40 years," said Ted Shaw, associate director-counsel of the NAACP Legal Defense and Education Fund. "But it's not too late to turn this around. The question is whether the commitment is there." Housing Tackling Root Of Segregation

The Civil Rights Act of 1968 gave members of minority groups the right to buy and sell property wherever they wanted. The notion was that creating integrated neighborhoods would lead to integrated schools.

More than 25 years later, the legislation has still not delivered on all its promises, in part because the Government has repeatedly subverted the plan. Even as Congress was approving the bill, the Department of Housing and Urban Development was building large public housing projects in inner cities, effectively concentrating huge numbers of minority families there. In the 1980's, the Reagan Administration's Justice Department allowed hundreds of complaints against biased real estate agents and landlords, filed under Federal fair-housing laws, to languish.