A decade ago, when ascendant black politicians began to take control of important city halls across the nation, it seemed that history had played a sardonic joke on them.

Now that the cities are dying, it was said, the blacks can run them. Some put it this way: now that the cities are going black, America will allow them to die.

This empty inheritance seemed especially hopeless in Detroit, a ruined place. It was visibly choking on crime and decay and racial fear when Coleman A. Young became its first black mayor in 1973.

Detroit citizens, in a perverse twist of hometown pride, used to entertain visitors with the latest horror stories - an especially chilling anecdote about street crime, another factory closing, another downtown store fleeing to the suburbs with its white customers.

The new mayor, narrowly elected by black voters with only a silver of support from whites, did not seem like the sort who would lead Detroit to the resurrection. He is by nature a provocative politician, blunt and casually profane. He often speaks with a wink in his voice, using bleeps and blanks and street phrases like "kick ass."

Black citizens understand and smile; white citizens tend to be alarmed. Just recently, the Detroit News denounced him again, this time for demagoguery on the issue of affirmative action. What Mayor Young said was this:

"Some people say affirmative action is discrimination in reverse. You damn right. The only way to handle discrimination is to reverse it."

Coleman Young had a reputation, well earned in his youth, as a troublemaker. Proud, belligerent, full of himself. A b-b-ad dude, in the current idiom. Young was a labor organizer and days of Detroit's past. He was at days of Detroits's past. He was at the the barricades on the race issue a generation before it became fashionable. He became a red pariah, blacklisted by the auto companies and by the auto union.

Yet today, the talk of Detroit bubbles along proudly on twin themes - the city is rising from the ashes, as local T-shirts proclaim, and the powerful mayor is building the "Young Machine" as he restores faith in the city's future. Coleman Young, the streetwise agitator, has convinced Detroit that it isn't dying, after all.

Allowing for the hyperbole of local boosterism, the optimistic chatter is basically correct. Detroit, which was in ruinous decline for at least 15 years, has turned around. Employment is climbing; crime is declining. The city's vital signs are improving modestly now and the downtown is noisy again, not only with new night life, but expensive projects, from the plaza and arena on the riverfront to shopping malls to the most crucial element of all - new intown housing.

This is a high-risk juggling game that Young is playing, hustling public and private money for an extra-ordinary array of projects, simultaneously. Another recession in automobile sales or a sudden resurgence of street crime and racial tension could wipe him out. Even if he succeeds, it will take a generation at least to restore Detroit to a self-supporting economic balance.

But cities like Detroit and Washington, D.C., and Baltimore and Atlanta and San Francisco are showing new life because they finally have some economic and social factors pushing in their favor. One is the energy alarms and the rising cost of transportation. Another is the extra-ordinary inflation of home prices in the suburbs. Young people are discovering that they can buy a fine old home inside Detroit for $30,000, fix it up a bit and have much more than they could buy for $70,000 in the distant suburbs.

Across the nation, blighted cities are beginning to be regenerated, some slightly and some dramatically. Old neighborhoods are undergoing rehabilitation and, in some places, the long exodus of white citizens appears to be reversing. The deep problems of poverty and decay remain, but this trend is an encouraging contradiction of the gloomiest forecasts made a decade ago about black politics and towns like Detroit.

As for the major, whether they love him or despise him, citizens talk about Coleman Young the way Chicagoans used to talk about the Boss, the late Richard J. Daley, with wonder and resentment, respect and envy. Young does not have a "political machine" in the classic sense, but the basic elements of his leadership are quite similar to Daley's. Young mobilizes power by spreading sugar and concrete and good talk - by delivering jobs to his people, enticing business back with tax breaks, building improbable coalitions that seem to work.

"Daley was a good man," Mayor Young said, acknowledging the debt. "You can go to Chicago and learn. Chicago is one big city that's been relatively immune to the deterioration other big cities have suffered. A lot of this is attributable to the coalitions Daley put together."

Young understood at the outset what other mayors, white and black, have learned the hard way: in every community, City Hall only has a piece of the power. A collection of non-elected interest groups, from bankers to union bosses to cops, govern the city too, directly to discreetly. They can veto or endorse, obstruct or stimulate, depending on how the mayor approaches them. Confrontation politics was an effective tactic of the civil-rights years, but it can weaken a mayor, if he's not careful.

"My responsibility," the mayor explains, "is not to create a condition of anarchy where the city self-destructs and blows apart, where the state puts the city in receivership. Everybody has a mutual self-interest in the city and that's what I have to deal with - to try to show them their mutual self-interest."

This surprised many people who remembered Young's fractious youth and expected him to go head-to-head with the industrial powers who dominate Detroit. They misunderstood the lessons he had learned.

In many respects, Mayor Young's 60 years provide a neat synopsis of black struggles in this century, the bruises and the triumphs. He was born in the South, in Tuscaloosa, Ala. At age 5, he came north with his family to the boom town of Detroit.

Millions of black families made the same journey to the industrial north, a great migration that began in World War I and reached its peak after World War II. In 1890, 80 percent of black Americans lived in rural poverty; by 1970, 81 percent lived in urban areas.

Until quite recently, the black migrants were the last great immigrant group to reach America's cities. Though they had been in the rural south for 200 years, they came to the cities as aliens, long after the Germans and Irish, the Italians and Jews and Poles. Like those other groups before them, they were consigned to the bottom, in the worst jobs and neighborhoods, politically powerless.

In addition to the white racial fears, their presence threatened the economic security of workers who preceded them - by providing industry with a new supply of cheap labor - and Detroit suffered two of the bloodiest race riots in American history. In many cities, including Detroit, blacks are now being replaced at the bottom by the new wave of Hispanic immigrants. Among some black workers today, one hears the same slurs and complaints about "Mexicans" that used to be directed at blacks.

Coleman Young's father did not make it into the auto plants. He worked as a night watchman and ran a small clothes pressing shop in the Black Bottom section (across the street from the House of Diggs, the funeral home which spawned the political career of Rep. Charles Diggs, the Democratic congressman).

When Coleman finished high school, he did not go on to college, though he was a bright student. There were no scholarships available in the 1930s for "colored boys."

At the Ford plant, where he went to work, Young was caught organizing for the union. A company man came after him and Young bashed him with a steel bar. He was fired.

During World War II, he joined the Army Air Corps' elite black outfit, the Tuskegee Airmen, and was among those arrested for demonstrating against the segregated officers' clubs. Once, while flying over Tuscaloosa in an Army plane, Young tried to urinate on his birthplace as a gesture of contempt for its code of segregation.

After the war, he got kicked out of the union too. He was tagged as a communist when the United Auto Workers was purging its left-wing members. In those days, the mayor explains, the Left was the only element of organized labor which was out front on equal rights for Negroes.

Young thumbed his nose at the House Un-American Activities Committee and disbanded the National Negro Labor Council when the attorney general put it on the "subversive" list and demanded its membership rolls.

Blacklisted in the auto industry, Young scuffled for years on the fringes of labor organizing and politics. He pressed pants, drove a cab, eventually prospered modestly selling insurance. And, despite the opposition of the established powers, Young found his way onto the political ladder.

Elected to the state Senate in the early 1960's despite the UAW's opposition. Young became the Democratic floor leader, a tribute to his political skill in a state which was only 10 percent black. In 1973, he defeated the UAW's white liberal candidate for mayor, then went head-to-head against the white law-and-order candidate, a tough police commissioner known as "Black Jack" among the black citizens. He won narrowly - but the city was racially divided, broke, despairing.

At that crucial juncture, Coleman Young, the old radical, sat down with capitalist barons like Henry Ford II whose company men had crushed him, and with the UAW leaders who had made him an outcast. Together, they agreed on this: they needed each other.

A Detroit cynic described the coalition crudely: "Coleman Young needs Henry Ford to stay mayor and Henry Ford needs Coleman Young to keep blacks peaceful."

Remer Tyson, political writer for the Detroit Free Press, describes what has happened in Detroit politics as "the integration of power," which means white power is dealing with black power on a reasonably equal footing, not as a charity case.

Young charmed the silk stockings off the industrialists. When Max Fisher, the Republican millionaire, needled him once about some public inconsistency, Young replied saucily: "Don't forget, I'm a Marxist." Max Fisher is planning to build new apartment towers downtown, 2,100 units.

Last year when Young was up for reelection, Henry Ford II sponsored a $1,000-a-ticket fund-raiser at the establishment retreat, the Detroit Club, and gave his public blessing. "Coleman Young is my favorite mayor," he said. Young responded with a grin: "And Hank the Deuce is my favorite industrialist."

Young won reelection in a landslide against a black opponent, City Councilman Ernie Browne, whom the mayor derided as "the first black white hope in history," after Browne was endorsed by the white cops of the Detroit Police Officers Association. Young had business, the unions, the black churches, Democratic Party workers pulling together in his campaign, an election-day army of 5,000 volunteers. A majority of white citizens still voted against Young, but many simply sat out.

Browne, a former Eagle Scout and a church man, tried to make an issue of the mayor's lifestyle - two divorces, a beautiful girlfriend, a taste for fine clothes and good whiskey and Caribbcan vacations. When the last Cadillac convertibles rolled off the assembly line, a historic moment for Detroit. Coleman Young bought one. The mayor responded to Browne: "I'm very suspicious of some son of a bitch who wears his religion on his sleeve."

Young's out-front style is part of his popularity, of course. It matches the tone of Detroit, a working-class town where union people and industrial managers have always spoken bluntly to one another. What Coleman Young learned in his early struggle is what he told a Free Press interviewer during the campaign:

"I never looked upon myself as a do-gooder because a do-gooder is someone who out of a sense of noblesse oblige or some kind of s - like that reaches up and pulls some poor benighted son of a bitch and does good for him. What I've done is in my own self-interest. It serves to validate my own personal sense of worth and dignity, as a black person, as a poor person, a person of working-class origin."

Identify your own self-interest. Identify the self-interests of others with power. Figure out how they can be made to work together. "Anyone who knows me," Young said, "knows that I've been building coalitions all my life. In labor organizing, that's the only way you ever get anywhere."

Henry Ford - or Hank the Deuce, as black auto workers call him - speaks and operates with a bluntness similar to Young's. His own contribution to Detroit's revival is the $300 million riverfront colossus, the Renaissance Center, a hotel-office complex which was built and filled by Ford's not-so-subtle clout in business and finance. One of the five towers is occupied by the Lincoln-Mercury Division because Ford ordered it to relocate from suburban Dearborn to downtown Detroit.

"I don't think there's anyone more responsible for the turnaround than Coleman Young," Ford said. "The city's 50 percent black and we had to have a black mayor and, as long there was going to be a black mayor, he's an excellent one.

"He really knows the game. He plays the black side. He plays the white side. He plays the business side and the labor side. That's the game. He's smart enough to know the establishment route. Some people aren't smart enough to go that route, but Coleman Young is. He plays both sides. Goddamn, it's just remarkable."

American politics makes strange buddies. Henry Ford goes about the country warning that America is "on the road to socialism" while Mayor Young predicts, confidently, the same thing.

"I do believe we're going to eventually have some sort of socialism in this country and around the world," the mayor said. "It will be an Americanized version. It won't come out of any textbook."

In the meantime however, Coleman Young is playing by the capitalist rule. That means generous tax incentives to convince private business that downtown is a good investment. He created a special taxing district for downtown that willl recycle the increased revenue from new business into more public developments for downtown. He had enacted a 12-year property tax exemption for new construction - derided by critics as the "Max Fisher Bill."

"I don't give a f . . . who benefits", the mayor said. "I hope there are 10 Max Fishers who take advantage of it and build downtown. I see nothing wrong with Max Fisher or Henry Ford or Joe Blow making some money if they come into the city. They're going to spread some of that money around."

Young's belief is that some day America will adopt national planning - one of those socialist ideas Henry Ford dreads - that would eliminate the costly competition in which one city or state tries to steal factories and jobs from another part of the country by offering tax sugar to corporations.

"Those are the rules now and I'm by the goddamn rules," Young said. "This suicidal outthrust competition among the states has got to stop but, until it does, I mean to compete. It's too bad we have a system where dog eats dog and the devil takes the hindmost. But I'm tired of being the hindmost."

From the Left, there are muted questions about his strategy as mayor. If Young does not confront the "fundamental contradictions" of the economic order, will there by any real change for the poor blacks of Detroit, who still live in a sinkhole of poverty?

Councilman Kenneth Cockrell, an independent socialist, proposed a $100,000 feasibility study for a city takeover of Detroit Edison. Young vetoed it. He supports public ownership of utility companies, he explained, but not when it would cost $1 billion that Detroit doesn't have.

Rep. John Conyers, the Democratic congressman, offered a sympathetic critique of Young's political alliances:

"The question is: has he been coopted or has he finessed them? Who's coopted whom? I'm not sure. I was very skeptical at the beginning, but I'm more sympathetic now.

"First of all, if you don't get downtown going, nobody's going to believe you. Coleman's first and major battle was to get enough people to believe the city can be saved. So far the net result is that he's winning. He didn't make the mistake that Stokes made in Cleveland [former Mayor Carl Stokes, first black mayor of a major city] by alienating these groups and putting himself in a corner. The big business guys can cut your b . . . off."

Young has his own answer: "If I was coopted, I was certainly willing. It's just like the gal who got chased by the guy until she let him catch up with her. I don't know which one of those roles I fit, but one of them."

Beyond the coalition-building, Young's strategy is based on other important rules of urban politics, rules which old-fashioned mayors like Daley of Chicago understood. Running a city hasn't changed that much from the "machine" era. Here are the rules:

Take care of your people, the folks who elected you. Young's direct patronage is limited, but he has managed, nonetheless, to change City Hall's complexion.

He calls himself a "50-50 mayor" and his administration carries out the white-and-black balance explicitly at every level, from his office secretaries and bodyguards to department heads and recruits for city jobs and police. The 25,000 city employees are now 55 percent black - and 27 percent female. Blacks on the police force are up 35 percent, including the chief and nine of the 21 district commanders. The mayor lost the first round of a lawsuit challenging his method of promoting blacks to police sergeant - by jumping them up the promotion lists - but he makes no apologies.

"I've lost a lot of my conservative allies on that one," he said. "I've been very careful to balance the damn thing because that's the only way we're going to build a sense of community."

With the leverage of City Hall, Detroit's black community is also producing a new cadre of young professional leaders, politically attuned to Coleman Young's rebuilding dreams. Chuck Davis, a planner, directs downtown development plans for apartments, shopping malls, parking garages, among other projects. Henry Hagood, a builder and political fund-raiser, controls more than $10 million in city contracts. David Lewis' law firm handles the city legal business. Three of Young's top aides from City Hall are "on loan" to Cabinet officers in Washington.

These political bonds spread across the city, from the church pulpits to the UAW offices, many of whose black officers helped elect Young in 1973, despite the union's formal opposition.

One of them, Robert (Buddy) Battle, head of UAW Region IV, predicts: "Unless they catch him doing something awful bad, I think Coleman can last at least another eight years if he wants."

When the mayor turned up at a recent fund-raiser for Congressman Diggs, who is under federal indictment for payroll kick-backs, Young gave the communal blessing: "We are not behind you. Charlie. We're beside you."

Diggs responded: "My special thanks to the Godfather."

Choose your enemies wisely, if you must make enemies, for maximum political value. Coleman Young chose the white police, a powerful and conservative political force in Detroit. When white fear was rising, the police were virtually at war with the black community.

The DPOA has opposed Young at almost every turn. The association is still run exclusively by white officers and the mayor regularly calls it "out and out racist." Last year's election demonstrated that he had beaten them, politically.

"He owns the city." Jim Van Devender, DPOA president conceded. "He's street wise. He knows what his supporters want to hear. We find that, to a fine art, he's not beyond half truths, but by sheer numbers, he's got us."

After three very turbulent years, marked by roving gangs and some vicious episodes of street crime, the city's crime is now subsiding. The police were reorganized, dispersed on foot in neighborhood mini-stations, under a black chief and a highly regarded white deputy.

"The policemen were literally taking over our cities," the mayor said. "We were getting police cities. There were cops running for mayor everywhere. Certainly that was one answer. I perceived control of the police and having the police reflect the community as the key to getting control over crime and having a real community."

In time, as the 50-50 mayor continues, the DPOA will undoubtedly elect some black officers. "Eventually, the blacks will assume leadership of this union, by sheer numbers," Van Devender said. "I'm not a predictor of gloom. I don't think the union will collapse."

When that happens, the last strong political counterforce, representing the majority of whites in the city, will be gone.

Do not speak ill of other politicans whom you need. Coleman Young's cozy relationship with Jimmy Carter is another improbable alliance, the pious president and the profane mayor, but crucial for both men.

Young was the first important black leader to endorse Carter's candidacy and he remains loyal. When Urban League executive director Vernon Jordan attacked Carter's urban program, Mayor Young put Jordan down hard. "Some people run their mouths," the mayor said, "and some people run cities."

If Carter needs Young politically, Detroit needs the federal dollars even more for survival. Like every major city, it depends upon federal aid, both to pour concrete and spread pay-checks in the community, and will for a long, long time. Young, like Mayor Daley during the Kennedy and Johnson years, has concluded that he can get more from Washington standing by the Democratic administration, instead of attacking it.

For similar reasons, Coleman Young gets along fine with the Republican governor of Michigan, William Milliken. Detroit needs Lansing for aid and legislation. Nobody expects the mayor to be too zealous about opposing Milliken in this year's state election.

Talk in a language that will reassure your people, even if it provokes your opposition. This has been a hallmark of every important ethnic politician, from Mayor Curley of Boston to Daley of Chicago. The only difference with Young is that he talks black.

At his inaugural in 1973, the mayor proclaimed in colorful language his own version of law-and-order - aimed at police crime as well as street crime.

"I issue an open warning right now to all dope pushers, to all ripoff artists, to all muggers." he said. "It's time to leave Detroit. I don't give a damn if you are black or white, if you wear Super Fly or blue uniforms with silver badges, hit Eight Mile Road."

The white suburbs went wild. Eight Mile Road is the city boundary and uptight suburban mayors thought Young was telling black hoodlums to go rob the suburbs. The white police didn't like it much either, being lumped with dope pushers.

But the new black majority of Detroit understood him. They thought it was amusing that whites were so provoked. Every time the editorial writers attack Coleman Young, black citizens are reminded they finally have a mayor speaking their language. CAPTION: Picture 1, Detroit Mayor Coleman A. Young and downtown Renaissance Center, a $337 million symbol of city's rebirth. AP; Picture 2, Mayor Young, Vice President Mondale and Henry Ford II dedicating Renaissance Center in April 1977. AP; Picture 3, COLEMAN A. YOUNG . . . self-interest, not anarchy; Picture 4, ROBERT BATTLE . . . union boss, mayor's backer; Picture 5, CHARLES B. DAVIS . . . city redevelopment planner; Picture 6, KENNETH COCKRELL . . . his socialism rejected