The Alexandria School Board yesterday selected Robert W. Peebles, a soft-spoken educator from Connecticut, to head the city's schools, a system beset with the same declining enrollment and racial balance problems he confronted in the New York City suburbs.

Peebles, 54, head of Stamford, Conn., schools, will assume the $55,000-a-year position Aug. 1, replacing John L. Bristol who resigned earlier this year.

"Stamford is very similar to Alexandria in size and makeup, which had a lot to do with our choice," said School Board Chairman Alison M. May as she announced the appointment. "I'm delighted that he is coming here."

The decision to select Peebles, who holds a doctorate from New York University and a master's degree from Harvard, came at a closed meeting of the school board and was not unanimous, officials said yesterday. Under Virginia law, the school board is allowed to meet in private to discuss personnel matters, although it is required to vote in public on Peebles' appointment, an action expected at next Wednesday night's board meeting.

According to William D. Euille, a member of the school board, three people -- Peebles, a white woman, and a black man -- emerged as the top finalists from 174 candidates in 33 states and the District of Columbia who applied for the position.

After several votes during Saturday's sessions, it was clear that Peebles was the choice of a majority on the nine-member board. Euille said he did not vote for Peebles because he favored another, unidentified candidate.

The final vote on the selection could not be determined yesterday. May declined to discuss the question, saying only that the discussion had occurred in "executive session.

Euille, who opposed Peebles in the private meeting, declined to say how he would vote on the question in public. "But I think he's an excellent man for the job and will do well in Alexandria," Euille, a building contractor, said.

The problems Peebles will face with the 11,000-student Alexandria school system are similar to the problems he faced during his five years as head of the 16,000-student Stamford system. Those problems include declining student enrollment, the possibility of closing neighborhood schools, and private concerns about racial harmony.

The population of Alexandria's school system has dropped from 18,000 in 1970 to about 11,000 today, a drop attributed in part to a busing plan used to achieve desegregation of the system.

Several schools have closed in the past few years, because of the enrollment decline, including several in black neighborhoods that have prompted protests that the schools there are being closed at the expense of schools in white neighborhoods. Maintaining a balance of both white and black students in the Alexandria system, currently 48 percent black, has been a top priority of the school board.

In Stamford, Peebles said he supervised the closing of three neighborhood schools "without incident," and developed "magnet schools" to attract students to the system.

Peebles said at a press conference yesterday that his "first impression" is that his top priorities will be to deal with declining enrollments, maintain the current racial balance and increase the quality of education. "I have a strong bias that city school systems can compete with suburban school systems" for quality teachers and programs, said Peebles.

His introduction to the school system's top staff members yesterday provided veteran Alexandria administrators with what several said they hoped would be a continuing contrast with the three-year regime of Bristol.

"I think we are in a new era of human relations with Peebles," said one high-ranking administrator after meeting him in a closed-door session. "We are a people-centered operation, students, teachers, and administrators. Bristol never realized that we are not a factory," the official said, asking to be anonymous.

Bristol, who came to Alexandria in 1977, resigned last January to take a higher paying job in Illinois. During his tenure he frequently was criticized by teachers and some city officials for his aloofness and apparent lack of interest in their problems. Other school officials praised him for the sharp managerial policies he brought to the school system, whose budget has been increasing each yeear while its enrollment declined.

Bristol did not attend the news conference given for his successor. May said he was out of town and could not be reached.

Richard G. Weber, president of theStamford Board of Education, yesterday said Peebles was a good adminstrator "whose greatest strength is his ability to work with people, and whose greatest weakness is an occasional inability to put is foot down and make a decision."

Weber said Peebles is a "low-key individual . . . whose personality makes the community feel more stable." He said Peebles had a good rapport with black leaders "although some blacks have criticized us for not hiring enough minorities in the schools."