The inner cities of America are poised for a stunning comeback, a turnabout in their fortunes that could be one of the most significant developments in our national history.

The recovery from decades of middle-class desertion, housing abandonment and intolerable levels of poverty and crime will not be a smooth or tidy process. The cities' renewal may trigger social discord as the affluent and the poor fitght for their share of the urban turf. And there surely will be backwaters of urban desperation for years to come.

But talks with a cross-section of the nation's mayors, meeting here at the annual U.S. Conference of Mayors, plus grass-roots reports from many cities, present a phalanx of evidence that the critical mass needed for city recovery has finally fallen into place.

The chief ingredients accelerating middle-class return to the cities are the energy crisis, the explosion of the post-World War II baby boom into the new household market, changing lifestyles and mounting dissatisfaction with suburban life - especially among young people.

All this is complemented by out-of-sight single-family home costs, the economies of restoration over new construction, shifts in federal policy away from the pro-suburb bias of the last three decades, the strong and growing national neighborhood movement and a pronounced decline in urban crime. The result a new hope in the city that breeds fresh investment and confidence.

The nation's capital, where federal payrolls fuel a vigorous economy, is the vanguard of the back-to-the-city movement. Young, upwardly mobile singles and couples - whites and blacks alike - are penetrating one inner-city neighborhood after another, even some wracked by the riots of 1968.

But Washington is not alone. In Baltimore and other cities, housing abandonments are dropping off - often to the vanishing point. In Chicago's middle-class areas, Mayor Michael Bilandic says, there's a sudden upsurge in property values, far beyond what the market would normally justify. Other cities reporting the same resurgence include Boston, Louisville, Pittsburgh, Houston, Portland, Seattle, New Orleans, Atlanta and New York.

even in heavily black Gary, Ind., Mayor Richard Hatcher notes an incipient middle-class return. In Detroit,, considered a classic urban "basket case," Mayor Coleman Young reports that "for the first time in years, you find white middle-class people mingling with blacks shopping for houses in the better neighborhoods."

The cities are now well past the first wave of renovation in blue-chip areas like Washington's Georgetown, Brooklyn's Park Slope, Philadephia's Society Hill and New Orlean's French Quarter. Now the upswing is spreading to hundreds of less-fabled neighborhoods - often because of their architectural distinction or premier locations. Residential restoration is no longer limited to townhouses, it's expanding into old warehouses, factories and wharf and tenement building, the urban residue of the industrial revolution.

Read Census Bureau reports alone and you'd never believe a revival was under way. The Census's 1970 to 1975 population-shift estimates showed a continued, massive hemorrhaging of city population: St. Louis losing 1 out of every 6 residents: Cleveland 1 out of 7; Minneapolis, Detroit and Buffalo 1 of 8; New York 1 of 19. The 1975-to-1976 center-city loss was estimated at an incredible 2 million people.

But mayors dispute the Census estimates and insist their cities are at least holding their own in population. They may or may not be right, but total population may not matter so much. Demographer George Grier has discovered, in a study for the Washington Center of Metropolitan Studies, that while Washington lost 55,000 population between 1970 and 1975, the number of households remained virtually constant. But in contrast to the larger family units they replace, such new households are small - consisting of never-married singles, newly divorced people, couples (married or not) who are delaying parenthood.

Boston, Seattle and New York studies suggest the same: smaller households, made up of children of the baby boom that helped trigger the post-war rush to suburbia, now returning to the city. Fiscally, that's good news for cities, because the returnees enrich the tax base without costing much in schools, welfare or other services.

Indeed, the cities needed attract only a modest percentage of the record number of new households now information to compete - as urbanologist Paul Porter puts it - "even with their strongest suburbs as a place to live."

The Hartford City Institute reports the city-bound flow of middle-class immigrants "is still a trickle, but a growing one that might become a flood," Hartford Councilman Nichilas Carbone says it's made up "first of the youth, who find the suburbs boring and that the city's where the action is. The youth have guts, they're less prejudiced than we are and they'll move into integrated neighborhoods. They're followed by the liberal part of the establishment that's gone through middle-aged menopause and is also enchanted with this new lifestyle."

The cities also argue economy: Rehabilitation costs generally run only 50 to 60 per cent of the price of new construction because the work is less extansive and doesn't involve site preparation. Rental and purchased prices - until a city becomes too popular - are well below suburbia's. Mortgages are becoming - are to obtain as legal and community pressures beat down redlining and as lending institutions form mortgages pools of inner-city rehabilitation and purchase. Recent revisions to the federal tax code favor rehabilitation and historic preservation.

Only six years ago, Columbia Professor Eugene Raskin wrote that cities "are physically obsolete, financially unworkable, crime-ridden, Garbage-strewn, polluted, torn by racial conflicts [and] wallowing in welfare unemployment, despair and corruption." He suggested they were "unsalvageable" and deserved extinction."

Eat your heart out, Mr. Raskin. There's a new day dawning.