In a recent talent show at Alexandria's T.C. Williams High School, one highlight was a skit about a girl in a shower.

A black girl came on stage wrapped in a towel, singing a parody of a soap commercial. She stepped behind a shower curtain and a few minutes later, out stepped a white girl, wrapped in the same towel.

The audience, both black and white, laughed and applauded loudly.

"They were kidding about race, just laughing about it," one parent said. "A few years ago nobody would dare do that."

The friendly laughter that greeted the skit, which might have been perceived as a slur, is one measure of how racial tensions have eased in Alexandria school after seven years of busing for desegregation.

The change in attitudes is significant. When busing began in 1971 there was sporadic fighting between groups of black and white students and police had to patrol the halls of several schools.

But along with gains have come some serious disappointments. Even though Alexandria schools now contain about equal proportions of white and black students, only a small number of blacks are taking advanced subjects.

Furthermore, there is no evidence to support early hopes that black students would make substantial academic gains as a result of desegregation.

What is most readily apparent about the city schools, however, has been massive white flight -- an exodus that the relatively high city school budgets, an academically strong central high school and an extensive public relation program have been unable to prevent. Today there are fewer than half the number of whites in the schools than there were in 1970.

Last fall the white enrollment dropped another 7.1 percent. But for the first time since the busing program began, the number of blacks in the schools fell sharply, too, and the overall racial balance emerged almost unchanged from the previous year.

Alexandria schools now are 48 percent black, 44 percent white, and 8 percent Asian and Hispanic. In 1970, just before busing started, the system was 70 percent white.

"I don't think busing is all pluses or all minuses. It's both of them," remarked Charles Beatley, an airline pilot who was mayor of the city when busing began. "People have been brought together, but it hasn't produced what some people hoped for -- a quality education for everyone. Has it been worth it? I think it probably was, but it's not a clear picture."

When busing started in Alexandria -- by vote of the school board but under threat of court action -- it was the first program of its kind in the Washington area and one of the first in the country. Later, Prince George's County was ordered by a federal judge to do the same thing.

Similar court orders have been implemented in hundreds of school districts throughout the South and recently in northern areas as well.

In Alexandria -- and elsewhere -- the process has turned out to be more complicated and its results more ambiguous than it first seemed.

For example:

Interracial friendships have flourished among young children in Alexandria, parents and teachers say, but among adolescents there is considerable separation.

T. C. Williams, which became a citywide high school as part of the desegregation plans, is so well regarded that it draws dozens of students a year from private schools. But in the city's junior highs serious academic and discipline problems persist.

Even though most classes have a broad racial mix, advanced academic courses are overwhelmingly white; remedial classes are overwhelmingly black.

According to teachers, black youngsters account for a high proportion of discipline problems. They are suspended twice as often as whites.

Even though the Alexandria school board adopted its busing program in hopes of avoiding court action, the board is now fighting a lawsuit by the National Association for the Advancement of Colored People. The NAACP charges that the city school board has discriminated against blacks in choosing which schools to shut as enrollment has dwindled to 11,797 this fall from a high of 17,786 in 1969.

Inside the schools, the patterns of race relations are complex.

"They're all just children here," said Christine Howard, principal of Alexandria's Jefferson-Houston Elementary School, as a line of youngsters passed on their way to the cafeteria.

There were small black and white children holding each other's hands, smiling and jostling occasionally, swinging their lunch boxes and sometimes straying too far to the side.

"White, black, Asian, it doesn't make a difference," Howard continued. "We're not focusing on race at all, and neither do the children."

At George Washington Secondary School a half mile away, the music was loud and the dancing frenetic. Both black and white students were crowded inside a basement room.

Most of the music was "black," as the students called it; so were most of those dancing. Afterward, the crew of student government members that cleaned up was almost all white.

"You can desegregate a school but to integrate it is something different," said Mark Howard, an assistant principal at George Washington. "The black and white youngsters get along much better than they did five years ago, but it's not totally integrated. How integrated is society?

"There are differences in language, differences in family structure, economic differences," Howard said. "You can't expect it all to break down inside a school."

For example, high school basketball teams and their cheerltaders are predominantly black. The rowing crews are almost all white.

At T.C. Williams, which enrolls all of the city's 11th and 12th graders, the football team plays under a black coach, Herman Boone, who was recruited by former school superintendent John Albohm when busing began.

When racial tensions ran high in 1971 the school won the state football championship. "That really helped pull things together," Albohm recalled.

The success of black athletes, he said, "has been a big thing that's tied black children into the school system. It's given them status that many of them don't get academically."

Even though Alexandria does not have a system of across-the-board ability grouping for all subjects, a great deal of academic grouping occurs.

In elementary schools, classes have a full range of student ability, but because of federal regulations the students who are furthest behind, a group that is predominantly black, are sent to special rooms each day for help under a federal program.

At T.C. Williams, where the course list looks like a junior college catalogue, many of the advanced classes in science, math and literature have only one or two blacks enrolled.

"We want to keep racially balanced as closely as possible," said Principal Robert Hanley. "But we have to take students where we find them. I think it's a much fairer system for the students rather than throwing them all together."

So far, academic grouping in Alexandria has aroused little opposition from blacks, although it has done so in Washington and many other desegregated school systems. Ulysses Calhoun, president of the Alexandria NAACP, said his organization has heard a few complaint about grouping and is studing the issue. "But we can't make a decision now," Calhoun said, "on whether it's equitable or not."

In general, Alexandria parents and teachers say there is a great deal of interracial contact among young children. But students become more conscious about race in fourth or fifth grade, when they reach ages 10 or 11.

By junior high school the racial divisions are pronounced -- in playground groups, social activities, and seating arrangements in the cafeteria. The groups often are determined by who rides the bus together, teachers say, and because of housing patterns, the buses often are for one race or the other. Alexandria's junior high schools also have the most severe discipline problems.

By senior high school, many of the most disruptive students have dropped out. There is much less conflict between blacks and whites, though considerable separation persists.

"We used to hope that having the students go to elementary school together would break down all the barriers," one black junior high school teacher said. "It isn't all working out that way. I suppose it's part of adolescence. There's an identity crisis: Who am I? In this society, you know, race is an important part of identity."

Since the first phase of the busing program began in September 1971, the number of white children attending Alexandria's public schools has dropped by more than half -- from 12,270 to 5,228. The decline partly reflects a decrease in births, which has occurred throughout the country, but much of it is clearly related to desegregation.

"It's the white flight pattern," said David Armor, a Rand Corp. sociologist who has published a study of the phenomenon in districts throughout the nation. "When whites can go to a different suburb which doesn't have busing, that's what they've usually done." (Neither the adjacent Arlington or Fairfax County school systems have busing for desegregation.)

According to Alexandria school board data, except for the two years when busing plans went int effect, white withdrawals from Alexandria schools have not been much greater than in the past. But the number of white children coming in has dropped substantially.

"It's a replacement problem," said former school board president Carlyle Ring. "It's hard to attract new white families."

Ring and other school officials suggest that real estate agents have "steered" white families away from Alexandria. "When people ask about schools, you have to tell them about busing," says one agent, who asks not to be named. "In a lot of cases, I guess, that's enough to get them thinking about some place else."

To try to boost enrollment, Alexandria officials have made presentations to real estate groups and distributed thousand of brochures about the attractions of the schools.

In interviews, a small group of white parents who have taken their children out of Alexandria schools said they left because of discipline problems, particularly in junior highs, and because of problems faced by "average students" who don't qualify for advanced classes or need remedial work.

Overall, about twice as many blacks were suspended last year from Alexandria schools as whites, a situation that prevails in many desegregated districts, accoring to the U.S. Civil Rights Commission.

A citizens study committee in Alexandria reported in 1976 that even though there was "no evidence of widespread discriminatory practice,... our suspicion... is that there are two standards of discipline being exercised one for blacks, one for whites."

School officials strongly denied the charges. They responded, though, by establishing a new discipline code with uniform punishments throughout the school system. Arrangements also were made for more in-school suspensions of disruptive students, setting them apart in special rooms than sending them home.

As for academic achievement, Dorothy Murden, the school system's guidance director, said students of different ability levels are performing as well in Alexandria schools now as their counterparts did a decade ago.

Overall averages in reading and mathematics declined for several years after busing began, from slightly above national norms to slightly below them.

At T.C. Williams High School, advanced courses have produced more students passing college placement exams than any other school in the Washington area. But average scores of all Alexandria students on college aptitude tests are significantly lower than those in other local school systems except for Prince George's County and Washington.

Although the school board keeps no records on achievement by race, the elementary schools with the highest proportion of blacks generally score lowest on standardized tests. At T.C. Williams this year there are no blacks among the 39 students in the honor society, and administrators say there has been no increase in the small number of blacks taking advanced courses in the past seven years.

On the other hand, the proportion of black high school graduates going on to college has climbed substantially, but this is part of a nationwide increase that has occurred in all-black schools as well as desegregated ones.

"I think busing has had some positive effects," said Shirley Tyler, one of three blacks on the nine-member school board. "People on both sides of town have found out there are civilized people on the other side... But there's still a lot of latent and not-so-latent prejudice in this city, and blacks still have a lot frustrations... I think we have a long way to go."

"The busing has become an accepted thing," said Ronald Uhrig, a white police sergeant whose daughter attends first grade. "A lot of people still don't like it. They live near one school and they don't like their children going all the way across town. But fighting the thing just doesn't have any effect, so why keep doing it? .... I guess time heals a lot of things."