Earlier this year, Catherine Liggins, the black general manager of WYCB radio, was walking down the hall on the top floor of the District Building toward the offices of the City Council. Part way down the hall, she met half a dozen stern-faced white men in business suits marching in the opposite direction, toward the office of Mayor Walter E. Washington.

For a moment Liggins fantasized that the city's white minority had seized control of the predominantly black city legislature in a pre-dawn coup and was now dispatching a delegation to demand that the only black mayor in the history of the nation's capital resign.

Liggins followed the passing procession momentarily with her eyes, then turned to her companion and raised her eyebrows in a mimic frown. "damn," she whispered, "they're back already."

The whites were not part of a coup; they were simply European officials enroute to an appointment with the major. But Liggins, like other blacks throughout the city, finds it difficult to joke about her fears of whites returning to power in city politics.

In many areas of black Washington, talk of local politics these days inevitably turns to the question of which race will control city hall in future years.

On Sept. 12, Democrats in this overwhelmingly Democratic city will all but seal the fate of the city's second election for mayor in more than a century, and --this time -- the winner undoubtedly will be black. All three of the major candidates in the crucial Democratic primary are black. Seventy percent of the Democratic electorate is black.

Yet there are those who fear that the District of Columbia is about to elect its last black mayor, signaling a hasty end to what they view as a precariously conceived and tenuously maintained political notion begun less than 11 years ago with the appointment of Mayor Washington.

"This is the last time a man can run and know he's going to win because he's black," said Flaxie Pinkett, a life-time city resident, a leading black real estate dealer, a close friend of the mayor and a racial moderate.

John E. Jacob, executive director of the Washington Urban League, talked about a certain "feeling" in the black community. The fear, Jacob said, is "that given the way the city is perceived to be run [by blacks] and given the migration of significant numbers of whites and middle-class blacks into the inner city, a trend is developing to move toward the election of nonblack officials."

Jacob's fears are based on his own perceptions of limited data available about the increasing white population in the city. They are perceptions that many whites and even some blacks are quick to reject. Such perceptions in the black community are also based on decades of uncertainty, distrust and even some admitted feelings of inferiority.

All of which might just as easily be dismissed as groundless and irresponsible speculation, except in politics perceptions are often as important as realities. And the fear of losing what limited black control there is in this city, a subject seldom raised publicly, is a constant backdrop to this year's elections.

In the view of those who fear such a loss, the omens seem obvious:

There is bitter infighting among the city's elected blacks, fighting so intense that for some it has shattered the dream of black unity in local politics.

The news media are seen as having trained much of their post-Watergate attention on the public and private affairs of black officials. The media are seen as making front-page scandals of what were [WORDS ILLEGIBLE]long time, the contention is, whites helped put friends and relatives on the city payroll, for example. But only when a flamboyant black man, former D.C. Department of Human Resources director Joseph P. Yeldell, was accused of nepotism and cronyism (never substantiated), was there a string of front-page articles, they say. And, the critics add, white department heads in city government receive more favorable coverage than their black counterparts.

The media response is that this city government is treated no differently than other local governments, that it is now an elected government accountable to its citizens and that the press by definition occupies a public watchdog role. Media representatives add that the Board of Trade is not the editor-general of the Washington media and there are no crusading journalistic hit squads out to pick off black leaders.

Another factor seen as inviting the election of a white mayor in the future is the inability of the city's black political leadership to agree to field a single candidate. Such black unity has been a long-hoped-for political goal in the wake of the civil rights movement. In 1952, when Bishop Shellwood E. Williams of Bible Way Church marched 400 of his supporters into a city firehouse to vote on behalf of averell Harriman's presidential candidacy, an editorial in The Washington Post took Williams to task.

"Bloc voting is repugnant to the democratic process," the editorial reads. "It will backfire on those who promoted it within the District, for it will surely be used by opponents of home rule as proof that District Negroes would vote as a racial group in future elections and not as individual Americans."

When the home rule government took office in 1975, there was a semblance of unity, but it disappeared with the first significant divisive issue -- Mayor Washington's proposal to increase the gross receipts tax.

By the spring of 1976, Del. Walter E. Fauntroy, on behalf of himself, City Council chairman Sterling Tucker and Council member Marion Barry, was standing on the steps of the District Building attacking Mayor Washington's administration as a [WORDS ILLEGIBLE] boil on the body politic," By the end of last year, the D.C. Democratic State Committee, which had only one year earlier been united in its opposition to the mayor, was hopelessly divided on its preference for his successor.

In a city where hometown instincts are sometimes high, Walter Washington, born in Georgia and raised in James-town, N.Y., is the adopted favorite son in the race. His ties to the established black middle class, which has traditionally produced many blacks who held key positions in the city, come through his graduation from Howard University and through his wife, the former Bennetta Bullock. Her father was a prominent [WORDS ILLEGIBLE] minister, and that has helped the mayor develop a base among politically influential church leaders.

Washington rose to prominence through one of the traditional routes of black upward mobility in this town --marathon government service.

The mayor has never nurtured a political protege. But if there is an heir apparent, many feel it is Sterling Tucker, nine years younger than the mayor and his running mate in 1974. Tucker, a native Ohioan who came here 22 years ago, has cultivated the support of many middle - and upper-class blacks who used to back the mayor, including key ministers like Bishop Williams (who broke with the mayor in part because he felt Washington had been in office long enough) and the Rev. Henry C. Gregory of Shiloh Baptist Church (who said there was no need for the church community to put all its support behind the same candidate).

Many businessmen consider Tucker "stable and safe" like Washington, but likely to run the government more effectively. "The ideal situation would be Walter's charisma and Sterling's administrative ability," a ranking member of the Board of Trade said.

Tucker has followed a different avenue to political prominence, working as director of the moderate Urban League during the civil rights movement. He has brought with him many of the liberal whites who supported the league as well as some businessmen who have sat by the door of the clubby and WASPish Board of Trade, including John W. Hechinger, president of the chain of home improvement centers that bear his family name, and William B. Fitzgerald of Independence Federal Savings and Loan.

Other businessmen supporting him are Board of Trade regulars like Thornton W. Owen of Perpetual Savings and Loan, and developers Oliver T. Carr and Joseph H. Riley of National Savings and Trust Co. Riley supported Washington in 1974.

Tucker is the preferred candidate of many young middle-class black professionals, high-ranking government employes and minority contractors.

Marion Barry, a 42-year-old former activist and co-director of Pride, Inc., is the most recent immigrant to Washington among the three candidates. He came here 13 years ago to work with the Student Non-Violent Coordinating Committee. To many old-guard Washingtonians, Barry represents young blacks who migrate to the city and compete for prestigious jobs. To others, he represents a leader of the militant generation that rebelled in the streets in 1968.

In many ways, Barry continues to stand outside the politically influential black middle class. He lives in a reconditioned rowhouse on Capitol Hill symbolic of the white migration, while Mayor Washington lives in LeDroit Park, the historic home of the city's older black bourgeoisie. Tucker lives on upper 16th Street, NW, between the "Gold Coast" and "Platinum Coast" neighborhoods that house many of the young black middle class.

Barry's political network includes activists such as his campaign manager and long-time friend Ivanhoe Donaldson. He is also a favorite among several rich, white and liberal city socialites including Nancy "Bitsy" Lee Folger, daughter of the late former defense secretary Neil H. McElroy, who was also chairman of the board of Procter & Gamble.

Some Barry supporters, such as white real estate dealers Jeffrey N. Cohen and Conrad Cafritz, are ambitious young businessmen looking for access to the mayor's office. "To them," noted one observer of business and politics in the city, "the importance of being important is of far more concern than theory, program, policy or philosophy."

The election may be as much a case of the District of Columbia at war with itself --racial skirmish and a class struggle -- as it is a forecast of the fate of black government here.

With no white candidate in the race for mayor this fall, the test case for the future of white political power could be D.C. School Board member Betty Ann Kane's campaign for an at-large city council seat. The contest has gotten off to a nonracial start of sorts. The overwhelmingly white and politically powerful Board of Trade passed over Kane and another liberal white, Marie S. Nahikian, and endorsed conservative black real estate man H. R. Crawford. Kane and Crawford are considered the front-runners in the contest and [WORDS ILLEGIBLE] for the Democratic nomination.

Kane's election would undoubtedly be an encouragement to white political hopefuls. She would be the first white elected to the council citywide. (She has already been elected twice to the School Board as an at-large member.)

Jan Eichhorn, a Capitol Hill political activist, thinks the Kane candidacy offers an interesting footnote to the unique nature of race and politics in the nation's capital.

"There's a feeling now of reverse discrimination and Betty has an uphill battle," Eichhorn said. "Whites feel you have to be superqualified to be elected. You have to be better than good. It's just the way things used to be with blacks."