Not long after he had been reelected Mayor of Alexandria in 1976, Frank E. Mann passed a note to City Manager Douglas Harman at the start of an all-day City Council meeting. Mann wanted someone to go out and put money in the parking meter where his car was parked.

A city official dutifully did so and discovered to his amazement that the Mayor's car was parked in front of a 20-minute meter. For hours, a line of city officials made certain Mann did not collect another of the many parking tickets he had been accumulating. Finally, as the hearing droned on, one official got the keys to the car and parked it in the mayor's private space in a nearby garage.

To Frank Mann's ctitics, the story illustrates what they perceive to be the Mayor's arrogance and preoccupation with the perquisites of his office at a time when Alexandria faces more pressing problems.

"He likes to thumb his nose at things now and then," remarked one observer of the mayor and the Alexandria political scene.

Whether they like him or not, most people who know the blunt-spoken Mann, 58, agree that he is no ordinary politician. A dashing figure who obviously feels comfortable in the role of mayor, he exudes confidence and decisiveness.

A man with a reddish face adn wavy, silvery hair, he has been in and out of Alexandria politics for more than two decades. Yet for all that experience, including two previous terms as mayor, even his friends have a hard time pinpointing the issues in which he has taken a lead. Invariably, the conversation comes back to baseball.

"It occurred to me one day that rather than to try to hustle this big league deal maybe we ought to try to walk before we fly," Mann says of his successful attempt last winter to attract a Class A minor league baseball team to the city. People who know Mann say he considers bringing the Alexandria Dukes to the city, one of his two greatest triumphs. The other was having Alexandria named an All America City in 1964.

"To me it's really a mystery what he's really doing, what he cares about. I don't know," says City Council member Beverly Beidler. "Maybe what it says to me is that he may not be really serious about the job." Why did he run for mayor if he doesn't play a strong leadership role?"

Several City Council members say privately that Mann oftern cuts debate short at City Council meetings and that he frequently treats them and the city staff, including City Manager Douglas Harman, with an air of disdain.

"He's not a considerate person," says Timothy Swett, a former City Council member who has known Mann since the two were undergraduates at George Washington University in the late 1930's and early 1940's. "I don't think he has the word 'thank-you' in his vocabulary."

The city Mann serves today as mayor has changed substantially from the one he headed during his previous mayoral terms from 1961 to 1967. No longer the sleepy Southern town controlled by a few businessmen-politicians it once was, Alexandria show signs of some big city problems on a small city scale.

According to the latest official figures, the city's population growth rate has declined, from 2.2 percent in the 1960s to just over half a percentage point for the years 1970 - 1974. And it is a population in trasition. The number of minority residents in the city has increased substantially in recent years.

Twenty-two percent of Alexandria's residents are black, many of them in the low-income bracket and living in public housing units. In the past five years, the number of families receiving aid to dependent children has increased 110 per cent, a far greater increase than in any other Washington jurisdiction. A 1974 report by the Washington Center for Metropolitan Studies showed that 7.7 per cent of Alexandria's population had annual incomes under $5,000, compared to 6.4 per cent in Arlington and 1.6 percent in Fairfax.

The number of students in the Alexandria public school system continues to decline, dropping two percentage points from June 1976 to June 1977. Nevertheless, blacks in the school system, many the children of welfare families, have increased an average of four percent a year while the number of white pupils has been dropping by 10 percent a year. In the last three months of the school year just ended, there was a slight increase in the number of white pupils in the system.

The phenomenal growth of the condominium market in the west end of Alexandria during the middle 1970s has brought new problems from owners who feel they do not receive adequate services from the city. The condominiums have also brought a new type of resident to Alexandria - young professionals who feel little kinship to the Old Town political and social establishment of which Frank Mann is so much a part.

Meanwhile, Mann attends to City Hall and the City Council chamber, where he presides over a council made up of seven highly independent people with diverse backgrounds and interests. Of the seven Council members, Robert L. Calhoun is the lone Republican. Council member Ellen Pickering and Mann were elected as independents. The rest are Democrats.

Because Mann does not hold another jobs, he spends much time at City Hall's situation which sometimes seems to add to the tension between him and city manager Harman, the two are not close.

Asked what he thinks of Harman, Mann would say only that "the manager is relatively young, extremely sharp, and I think he has a great deal of professional pride."

This spring, City Council members were irked and even offended when Mann, who claims to work about 70 hours a week for the city, left for a week's fishing vacation on the island of Bimini just as the Council was making final budget preparations. He returned in time to suggest that the real-estate tax rate be cut, an action that would have meant a $7 million slash in the budget. Mann also suggested that Harman make the painful decision of which services to cut.

Mann now denies that he ever made such a proposal and says that under the charter only the council can approve such cuts. He also calls the charges "a super cheap shot." But there is a room full of witnesses to the fact that he did make the proposal.

In a long interview, Mann brushed aside criticism that he has not been a strong figure in the city government. "People who say that don't know what hey're talking about. They are frustrated and never liked me in the first place, or they want to run for mayor. So what difference does it make?"

Mann says it is not his role to tell people how to vote, but adds that he told the other council members when they were first elected that he would not tolerate any foolishness. "If we can work together," the Mayor recalled having told the council, "I will be the nicest guy you ever saw, but if you toot your own horn I will not tolerate it."

A lifelong baseball fan who still recalls with pride the time in 1933 when he won a free ticket to the World Series between the old Washington Senators and the old New York Giants because he had sold more subscriptions to The Washington Daily News than anyone else, Mann pushed hard for a commitment from the Carolina League last December to give Alexandria a team franchise.

To his day, Mann insists that opposition to the team, which was strong in the Lynhaven section of the city where the baseball field is located, existed only in the media. "Find me 25 people who were against it. You won't find them," he says.

Mann, whose father owned Mann's Potoato Chip Company until it was sold to Sunshine Biscuits in 1957, was first elected to the Alexandria City Council in 1951 on a platform urging a business-like approach to government. That has been the constant theme of his political career, through two terms on the City Council, two terms as mayor, and two terms as a member of the Virginia House of Delegates.

"The evil of government," he says, is to think that every time you want to you can extract money from a captive audience." He points proudly to the fact tht in his previous mayoral terms the real estate tax was cut twice, and that during his current term it has again been cut twice.

There is a general perception in the city that Mann is wealthy, but the mayor says it isn't so.

In his first term as mayor, he did not accept a salary because he was under contract with Sunshine Biscuits at the time and said he did not need it. Instead, he used $21,255 thecity owed him and established the Frank E. Mann Municipal Educational Foundation Charitable Trust. Under the program, city employes take special courses or attend seminars related to their field of expertise.

Mann accepts his $8,700 a year salary now because, he says, he can no longer afford not to, but the original money in the trust has grown to $27,000 and the program for city employees continues. Mann's second wife, Anita, owns a store in the city where the mayor spends a great deal of time. Mann is divorced from his first wife, with whom he had one daughter, Patty, 29.

Already, Mann has let it be known that he intends to run for another term as mayor next year.

"Being elected mayor of the city comes too easily for him," remarked Mann's college friend Swett. "If he were opposed by strong candidates he might work a little harder."

But City Council member Pickering, has her own ideas about Mann's success in local politics.

"He's very frank, everything is right out on the table," she says. "But he is not a cruel man, and he is not crooked. And because he is not cruel and is not crooked, he can get away with murder."