NEW YORK, NOV. 10 -- Once envied as centers of vitality, American cities have become to many people symbols of depravity, violence and hopelessness.

Great societies and wars on poverty have come and gone over the last three decades with inner-city dwellers living in greater squalor and more obvious danger than at any time in American history.

The mayors of most of the nation's 35 largest cities arrive here Sunday for a summit on the deplorable state of urban America, hoping for the first time in years to formulate a plan that can win support from the rest of the country.

Few question the need for a new approach. Many urban leaders readily agree that they have failed to convey to state and federal officials and to American voters generally the importance of supporting cities.

Many others say that cities need an alternative to simply "passing the hat" in Washington, as if it were the only cure for their ills.

"We have a good story to tell," said New York Mayor David N. Dinkins (D), who convened this summit and hopes it will produce a decent sales pitch for metropolitan America. "We just haven't had the opportunity to tell it well."

They better start soon, many experts agree, because the signs of stress are nearly everywhere. The District's fiscal dilemma and its troubles with drugs and violence have received worldwide publicity. Philadelphia is closer to declaring bankruptcy than any American city has been in 50 years. Dinkins announced on Thursday that he would cut 5,500 jobs this year to fill a $400 million budget gap. Next year the deficit will be at least four times larger and so, almost certainly, will the cuts.

But it is not just the big eastern cities, with their aging hospitals, crumbling bridges and thousands of homeless paupers, AIDS patients and drug addicts that have been overwhelmed with the problems that the mayors will discuss here on Monday and Tuesday. (District Mayor Marion Barry was invited but will not attend.)

"We all have crime, we all have drugs and we all know that nobody in Washington seems to have any answers for us," said P.J. Morgan, the mayor of Omaha. "I think we have mostly gotten the message that we have to fix these problems for ourselves. Nobody else is going to do it for us."

"From New York to New Orleans, from Birmingham to Detroit and St. Louis, the punishing problems of cities are more severe than you could possibly imagine," said Richard P. Nathan, director of Albany's Rockefeller Institute of Government. "The institutions essential to stability and civility have deteriorated and, as problems get more intractable, people turn away."

While the word "bailout," with reference to cities, has gone out of vogue, its application to another pressing crisis has not gone unnoticed by city officials. "The savings and loan crisis certainly proved that where you have the will, the federal government can find the money for anything," said Anthony Shorris, former finance commissioner of New York City. "There is no question that the will for aid to cities is not there. We have housing budget cuts every year, federal education programs are mythical. The national drug program is a joke. These are the issues that cities confront and the federal government is nowhere on any of them."

Over the past decade, federal aid to cities fell by more than 75 percent, according to the National League of Cities. At the same time, federal support for low-income housing assistance fell from $32 billion to $7 billion.

"The year Ronald Reagan was elected, at least four out of every five dollars that went to the Internal Revenue Service came back in one form of aid to cities," said Frank Shafroth, chief lobbyist for the League of Cities.

"Two years ago, for the first time in this history of this country, more tax revenue went to foreign aid than to cities and towns. Most Americans still live or work in cities," he continued. "But somehow our leaders have decided it is more important to support foreign counties. Why can't we have a referendum on that?"

At the same time, epidemics of AIDS and drug abuse have struck hardest at the people and cities least able to respond.

In New York and many other cities, the idea of a "safe neighborhood" is almost completely dead. Communities such as the Norwood section of the Bronx, for example, long a pocket of stability at the northern edge of the city, are beginning to decay. Buses come less often, violent crime has inched up. Trash lies strewn across empty lots. Everyone knows that certain blocks have become "crack blocks."

"It's an insidious steady decline," said Jack Gootzeit, who for 33 years has run an institute here that cares for severely handicapped people. "There are cuts and then more cuts and then more cuts. As the funds disappear, the problems increase. I always viewed the city as the last resort for all who are deprived. Now I don't know what it's for."

"What you are really talking about with all these numbers is a world view," said Robert M. Hayes, chairman of the Coalition for the Homeless. "You can't put Band-Aids on every urban problem by writing checks and you can't write off the disadvantaged just because they seem so hopeless. I hate to be naive, but isn't it time for a little compassion?"

State aid has been unable to fill the gaps generated by the massive loss of federal funds and with the nation awash in red ink, few mayors hold out hope for a magical solution to their fiscal problems anytime soon.

"These people need to make it clear that if cities fail, so does the rest of the country," said Nathan Glazer, professor of education and social structure at Harvard University. "But cities have been almost arrogant in their insistence that people are dying and poor and the only way to save them is with federal assistance."

Glazer and many other urban experts say it is time for cities to cut costs, levy sin taxes to provide services and perhaps, most importantly, begin to assess what the essential municipal functions should be.

"Hospitals, police, education -- sure," said one New York City budget official. "But do we need to have the most expensive public housing program in the country? Should the subways run all night? Should the Parks Department be so extensive? Its got to be cut somewhere."

Urban population has declined steadily over the last decade, as the middle class has fled the crime, the poor schools and the broken streets of the inner city.

Desperate mayors have been forced to raise taxes, which push out many of the people and businesses that can afford to pay them. Increasingly, those who are left have no alternatives. In New York, more than a third of city residents are below the poverty level today -- 13 percent more than only a decade ago. Drug treatment centers, hospitals and shelters for the homeless have all suffered funding cuts.

The crunch puts pressure on all city services. Gootzeit, for example, says that for 30 years, his organization, the Institutes of Applied Human Dynamics, took any severely handicapped person who needed care. It was a social resource of last resort.

"That's over now," he said, sitting in his office surrounded by institutional gray file cabinets and desks that haven't been replaced in decades. "We can't afford to take many of the most severely disturbed who come here. Some will stay home. Their families will be disrupted and -- like it was 50 years ago -- desperate people will begin to hide their retarded children or turn them out."

Even the most distressed vision of the city includes diversity, challenges and opportunities that can be found nowhere else, however. A poll conducted by the City University of New York and released in time for this summit suggests that most suburbanites would be willing to pay increased taxes to cover housing for the poor, AIDS treatment and drug rehabilitation.

To get that money, urban specialists believe, the mayors must prove that more taxes won't just be poured down the drain in hopeless causes.