The number of black students in the Alexandria school system dropped this year for the first time in more than a decade, while the decline in whites, which accelerated in the early 1970s after a major busing program was begun, slowed considerably.

Although the system still has slightly more blacks than whites, officials said its racial composition may have stabilized after six years of rapid change.

"I think it's too early to know whether these patterns will continue," school board chairman Alison M. May said in an interview. "But it may be that things will be fairly stable here in the future - with possibly a small decline in blacks and a small increase in whites. We want out schools to stay integrated."

According to official enrollment reports, the Alexandria schools had 5,679 black students in June - 289 fewer than a year earlier, a decline of 4.8 percent. During the previous 10 years the number of blacks had increased by 81 percent.

The number of whites enrolled was 5,492 - down 5.1 percent in a year but a far smaller decline than the losses of 8 to 16 percent that had occurred each year since 1971 when the city's first major desegregation program began.

Overall, the Alexandria schools have lost more than half of their white students since 1970. But from March to June this year they added 56 whites. Officials said it was first three-month period during the decade to show a white increase.

"We can't be sure," said Dennis Leone administrative assistant to Superintendent John Bristol, "but we're wondering if it may be an indication of renewed confidence of white parents in the city."

Leone said most of the decline in black students was caused by the closing of the Shirley-Duke and Regina Apartments, two large developments of low-rent garden apartments which in recent years had become heavily black.

New owners of the apartments have indicated that they plan to renovate the buildings and charge higher rents.

In addition, board vice chairman Shirley N. Tyler noted that the birth rate for both blacks and whites has declined while renovation in the Old Town area continues to spread, with low-income blacks being displaced by whites who can afford to buy old houses and remodel them. "I think it's going to be the trend in Alexandria," Tyler said, "that more and more low-rent apartments and low-cost homes are going to be renovated, and poor families, most of them black, won't be able to afford to stay in the city."

Tyler said many of those who left the Shirley-Duke and Regina Apartments had to move out of Alexandria even though the city has a relatively large amount of public housing and plans to build more.

Overall, the Alexandria school system now was 12,172 students - 47 percent black, 45 percent white, and 8 percent Asian and Hispanic. This past year the Asian enrollment also fell slightly after rising steeply for six years.

Total enrollment in Alexandria schools reached its peak of slightly more than 17,000 students in 1970. The schools then were 71 percent white, 26 percent black, and 3 percent Asian and Hispanic.

Despite a 29 percent drop in school enrollment, the population of Alexandria has remained almost stable at about 110,000, as many singles and young couples have moved into new high-rises built along Shirley Highway.

"What's happening in Alexandria is quite similar to the pattern in big cities," said Eunice Grier, author of several major studies on black population trends. "Household size is declining. Old housing is being renovated. The same thing is happening in the whole ring of inner suburbs around the District. They're not suburbia any more in the traditional way.

Black enrollment in District of Columbia schools has dropped 18 percent since 1970. Meanwhile, the number of whites in Washington schools has been stable for the past five years, but at only about 5 percent of total enrollment.

Alexandria school board chairman May said that after the school system decided to undertake its busing program in 1971 "many white parents were frightened and decided to go elsewhere . . . Now they see that good education is happening, and parents who might have gone are staying put. We've tried hard to make the system attractive to all kids, to have the advanced courses for the kid who wants to go to MIT and to meet the needs at both ends of the spectrum."

In Prince George's County, the only other suburban school system with a major busing program, white enrollment has continued to fall sharply and black enrollment to rise. Prince George's schools are now 41 percent black compared to 25 percent black in 1972.