The slogan of the losing candidate in this month's Chicago mayoral election--"Epton for mayor. Before it's too late"--sounded much like the slogan of Atlanta's losing mayoral candidate in 1973--"Atlanta is too young to die." That sounded a lot like the losing candidate's slogan in Birmingham in 1979--"Don't let Birmingham become another Atlanta."

All three unsuccessful campaign pitches were made against those who subsequently became the first black mayors of their cities: Harold Washington in Chicago, Maynard Jackson in Atlanta and Richard Arrington Jr. in Birmingham.

Each slogan played on similar white anxieties yet was incapable of stemming a trend in major American cities that many say reached a high point with Washington's victory over Bernard E. Epton in the nation's second-largest city.

In the view of many, black mayors, long perceived primarily as exceptions in a predominantly white political world, are acquiring enough numbers and geographic breadth to emerge as a distinct center of political power with a unique base and agenda.

Only 16 years after Richard G. Hatcher of Gary, Ind., and Carl B. Stokes of Cleveland broke the big-city mayoral race barrier, an estimated 220 mayors are among the nation's 5,000 black elected officials, including 16 in cities with populations of 100,000 or more.

Blacks have been elected mayor in three of the nation's 10 largest cities--Chicago, Los Angeles and Detroit--and a strong bid is being made in a fourth, Philadelphia. New Orleans, Atlanta, Newark, Richmond, Pasadena, Calif., the District of Columbia and other large cities also have black mayors. Baltimore, the nation's ninth largest, remains the only city of 100,000 people or more with a black majority and no black mayor.

Some contend that if the trend continues, these mayors could rival or outrank the 21-member Congressional Black Caucus as the premier national black leadership group and wield greater power on national politics and public policy.

"It's almost the next level of sophistication in black politics," said Ann Lewis, political director of the Democratic National Committee. "It may be that the Chicago election has nationalized the election of black mayors."

National Urban League President John E. Jacob ranked the mayors atop black leadership, citing their clear constituencies and the national prominence many have gained while seeking vital outside support during campaigns.

"I see them as a true reflection of the increased national leadership in the black community," he said.

No black mayor has been victorious in such a large, vibrant and politically potent city as Chicago and sparked such high expectations as Washington, 61, who began his second term in Congress this year before winning an internationally watched, racially polarized contest largely on the strength of unprecedented black voter turnout.

"Harold Washington is unique because, without a doubt, Harold Washington is the most powerful black politician in the country," Gary Mayor Hatcher said. "What's more important, he is one of the most powerful politicians in the country. . . . It would be inconceivable that anyone who wants to be president next year would not have to come by Harold Washington."

Major factors that increased the number of black mayors were the Voting Rights Act of 1965, which led to enfranchisement of the millions of southern blacks who have elected the vast majority of black mayors, and white flight to the suburbs, which is leaving blacks as bigger political shareholders in numerous central-city areas.

Washington's victory April 12 highlighted a third factor that has been apparent since 1976: increased registration and voter turnout.

Some of the major cities with black mayors have relatively small black populations. These include Roanoke, with 22 percent; Pasadena, 21 percent; Berkeley, 20 percent; Los Angeles, 17 percent, and Spokane, Wash., 2 percent.

Despite paranoid politics in cities such as Washington, where blacks have often voiced fear of losing newly acquired power, no major black-majority city with a black mayor has subsequently elected a white.

In Cleveland, however, where blacks comprise about 40 percent of the population, Stokes served only four stormy years and was unable to deliver the office to a black successor.

No black mayor has followed him, Stokes said, because "there just hasn't been any single individual who represented a black community-wide figure who enjoyed white support . . . and took the time to build political coalitions."

Some of the major cities with black mayors--including Washington, Atlanta and Oakland--have had more than one.

When Washington is sworn in Friday, he will inherit many of the same municipal, political and psychological problems that have plagued other black mayors.

The Chicago police department is overwhelmingly white and is viewed as brutal by many blacks, and the new mayor is largely an outsider to the influential business community. The city has a multimillion-dollar budget deficit, and white taxpayers have virtually abandoned public schools. And, other black mayors add, Washington's stewardship is likely to be hampered further by his color.

"A black mayor is in a position of having to prove that he has leadership ability," Arrington said, "as opposed to a white mayor who goes into office almost having to prove that he doesn't have it."

Jackson, mayor of Atlanta from 1974 to 1982, said color-blind government was often elusive. "You think you've gotten to the point where people are dealing with you on merit and you realize that with every controversy, one part of town views it one way, the other part views it another way because you're black . . . . It's never entirely gone."

Black mayors contend that race often increases tension with police. Stokes said he never gained control of his police department as he went through four police chiefs in four years. New Orleans' Ernest N. (Dutch) Morial said he believes his race was a major reason New Orleans police went on strike just before Mardi Gras in 1979 in an effort to win long-sought collective bargaining rights.

"They didn't strike against the white man," Morial said, "and they struck me after I gave them the largest pay increase in history."

Eddie N. Williams, president of the Joint Center for Political Studies here, said the relationship between many black mayors and business communities has been stilted for several years because the mayors have not been members of establishment power circles and often act and speak differently than whites with whom they must work.

The pioneering atmosphere that surrounds some black mayors has advantages, according to John J. Gunther, executive director of the U.S. Conference of Mayors, who generally concurs with the assessment that black mayors have done a good job.

"In many ways," he said, "they have been able to get some talent that a white mayor wouldn't be able to get."

One of the most difficult problems Washington is likely to encounter is high expectations in the black community. Chicago blacks, like those elsewhere in the nation, expect a black mayor to increase jobs and delivery of services to blacks and bring them more into the governmental process in many different positions.

A study for the Joint Center for Political Studies found that employment opportunities for blacks have generally increased in cities with black mayors. During the 1970s, black representation on municipal work forces of nine cities with black mayors increased an average of 16 percent, the study found.

Some black mayors, including Washington's Marion Barry, have instituted aggressive minority contracting programs. Others, such as Detroit's Coleman A. Young, have launched affirmative action programs, enraging white-dominated unions in the uniformed services.

Yet many things are impossible in political and economic terms, black mayors say.

"The level of black expectations is geometric, while our capacity to deal with it is not even arithmetic," Morial said.

"The level of expectations far exceeds the ability to deliver because the black mayor has to make coalitions to maintain the position he is in and to build for the future," he said.

Arrington said efforts to equalize city services in various neighborhoods often are viewed otherwise by whites. "It is possible to be fair to both," he said, "but the pie is only so big, and all of the pie has been going to one community."

"You get great opposition from whites because you say you want to treat everyone the same," he said. "They have lived under a system where they have had a distinct advantage based on skin color . . . ."

Jackson, now in private practice with a Chicago-based law firm, said any new mayor must put priority on keeping the city fiscally sound, must stay super clean ("It's not going to be good enough to say his or her predecessor did what he is accused of doing"), not try to work miracles overnight, incorporate the entire population into his vision for the city and use common sense.

"The bottom line," he said, "is if you don't pick up the garbage, put out the fire, protect the people, have clean water, fill the potholes, et cetera, you're going to catch holy hell, whether you're black, green or white."