Three sleek new skyscrapers inch their way to completion in a five-block stretch of Madison Avenue, a tribute to the continuing popularity of midtown Manhattan as one of the world's most elegant and expensive addresses.

Beneath the skyscrapers--which will house such blue-chip tenants as American Telephone and Telegraph, International Business Machines and Continental Illinois National Bank--the city's water and sewer system decays.

Limousines clog the Wall Street area each day, whisking the captains of business to their appointed rounds, and each night the chauffeur-driven cars line up at Le Cirque, Regine's and the Plaza.

But the drivers take their passengers down the FDR Drive at some risk, for the major East Side highway is crumbling. The landfill underneath is slipping into the East River, and concrete chunks regularly break off from the ceilings of the drive's tunnels.

The Upper West Side of Manhattan, much of it slum or nearly so 15 years ago, is a startling example of the revival of Manhattan. Ramshackle brownstones have been converted into high-rent apartment houses. Rent-controlled buildings are being converted to cooperative apartments. Rents are soaring as young professionals move in, and chic restaurants and clothing boutiques are replacing the cleaners, shoe repair shops and neighborhood bars.

But the subways that rumble beneath the West Side--as well as those that course below the rest of Manhattan, the Bronx, Queens and Brooklyn--are becoming more dangerous and unreliable, even as the fare becomes more expensive.

On the surface, New York City, the nation's biggest metropolis, seems to have made a remarkable recovery from the fiscal crisis that took it to the edge of bankruptcy eight years ago. It ran a budget surplus of more than $100 million last year and expects a bigger one this year.

For nearly seven years, the nation's financial capital could not borrow a dime on its own, but last year its unaided bonds were so popular it raised the offering from $200 million to $500 million.

Between 1969 and 1976 the city lost 600,000 jobs. Since then it has added 160,000 jobs. Wages and prices have risen more slowly in New York than in the rest of the nation, and even the current recession is making itself felt less severely in New York than elsewhere.

But beneath these rosy developments lie some harsh realities:

* Ronald Reagan's New Federalism will pull hundreds of millions of dollars out of the city. Some of the funds will have to be replaced, and the city will have to decide whether it wants to take on programs the federal government will abandon.

* The city continues to lose valuable manufacturing jobs, the kind that for decades have enabled poorer Americans to pull themselves out of poverty. "It will be one of the city's problems in the 1980s," said Chemical Bank economist Thomas Spitznas. "What will happen to the continuing buildup of blue-collar workers who cannot be absorbed in the service industries?"

* And the budget nightmare may recur. Mayor Edward Koch projects a deficit of $850 million for the fiscal year that starts July 1. That deficit projection may be raised, depending on this spring's labor negotiations. More threatening by far is the city's need for between $30 billion and $40 billion during the next decade to rebuild its aging physical plant.

New York, always a city of contradiction, of rich and poor, glitter and grit, can provide both optimists and pessimists with plentiful evidence to support their positions. But nearly all observers agree that the situation is different than in 1975, when circumstances were so dire city officials were not even sure how much they were spending. In 1983, survival is no longer the issue.

Instead, New York faces the same issues and problems as nearly all Northeastern cities, though perhaps on a grander scale. Can New York return to long-term financial stability and provide enough services to make the city palatable both for the poor who have nowhere else to go and the rich who can afford to bypass the city's problems?

Can New York keep the middle class who own property, vote and, in general, make the city work and worry about its politics?

Koch, who reached unprecedented levels of popularity in 4 1/2 years as mayor by preaching and practicing the normally unpopular gospel of retrenchment, said he is prepared to cut city spending further if necessary.

But Koch, who plans to run for the Democratic gubernatorial nomination this year, is not anxious to trim services any further in the Big Apple.

"It's a Hobson's choice," asserted New York investment banker Felix Rohatyn, who has headed the state's Municipal Assistance Corp. for most of the years the state has been borrowing money on the city's behalf. "If they reduce services further when they are already pretty well strained to the limit--in sanitation, police and physical facilities--the city runs the risk of driving out people again."

Koch said he is aware that New York City can tolerate few additional service cuts. In an interview before his February announcement that he wants be governor, the plain-spoken mayor said his first term was concerned with getting the city back on its fiscal feet. His second term, which began the first of the year, should be measured by whether "you are better off in terms of services," he said then.

Uppermost in the minds of most New Yorkers are crime and subway service. Most Manhattan dwellers long ago resigned themselves to dealing with the noise, congestion, rudeness and dirt that accompany living in the crowded borough in order to enjoy the diversity of the nation's communications, financial and cultural capital.

"Without the diversity, New York would be Bridgeport," admits former deputy mayor Peter Solomon, now a top executive at the investment banking firm Lehman Brothers.

"I like knowing I can get a bagel or a paper within five minutes of my apartment at any time of the day or night," said a young musician who lives on the Upper West Side. "But I don't like worrying about whether it's safe to do it."

But most New Yorkers are neither upper-class professionals nor artists, writers and actors who can afford--or feel the need--to live in Manhattan, the borough most Americans think of when they think of New York. Most New Yorkers are middle-class workers--today more white-collar than blue-collar--who live in Brooklyn, Queens and the Bronx. They want and need a safe, reliable public transit system to get them to Manhattan, where most New Yorkers work. The city cannot survive without that system.

Crime, an urban reality, is probably no worse in New York than in most big cities. But as incessant daily headlines in the New York Post and the city's newscasts underline, New Yorkers probably feel more threatened by crime--especially brutal street crime that occurs in good areas and bad--than residents of most cities.

Koch, despite the coming budget crunch, has ordered the temporary hiring of 2,300 more police officers in fiscal 1983. Whether that will deter criminals is problematical; and the number of police on the payroll will begin to decline again in 1984 as retiring officers are not replaced.

Riders are shunning the subways in droves. Each fare increase (the fare has risen from 50 cents to 75 cents in the past two years and another increase is expected by summer) drives away hundreds of thousands of riders. Service continues to deteriorate.

Trains break down about twice as often as they did five years ago. Doors frequently fail to open. The signal and safety system on the more than 700 miles of track (450 miles of it below ground) is falling apart from age. (A signal failure last summer contributed to a fatal crash.) Transit officials made poor choices in recent purchases of subway cars. Maintenance is poor. And crime, harrowing above ground, seems even more threatening in the underground caverns of New York's subways. Few New Yorkers who can afford another form of transportation take the subway at night. Even some members of the transit authority board admit they shun public transportation.

It will take more than $11 billion a year for the next 10 years to rehabilitate the mass transit system, and billions more if transit authorities are going to build new lines to relieve overcrowding and keep up with population changes.

In addition, New York must find another $20 billion to $30 billion to rebuild the rest of its physical plant. It must replace much of its 2,400-mile water and 6,100-mile sewer system (much of it is more than 100 years old). The city also must repair its bridges; the Manhattan Bridge can sway several feet when a subway crosses, and cables snap on the Brooklyn Bridge (one killed a pedestrian last summer). It must repave a large portion of more than 6,000 miles of streets.

Koch is spending about $2 billion this year on capital improvements, probably just enough to keep the city from deteriorating further. Koch points out that this year's capital spending is the first step in a major 10-year program to rehabilitate the city. But many critics claim Koch's capital spending is too low and wonder where he will get the money the city needs. Koch counters that before he became mayor, capital spending was virtually nonexistent.

If the city cannot rebuild its subways, highways and sewers and remove some of the paralyzing aura of crime that distresses New Yorkers as much as it does casual visitors, it will lose more workers and the corporations that employ them.

Many major corporations, distressed by New York's high taxes and the deteriorating quality of life, fled the city in the early 1970s. They set up headquarters in suburban Westchester County, Connecticut and New Jersey, where the environment was more favorable.

Like the jobs loss, the city reversed the corporate exodus, too. As the suburbs became more crowded, they lost some of their luster. Taxes were raised as counties scrambled to build the support facilities needed for the new buildings. But recently, Harcourt Brace Jovanovich, a major publisher, announced it would move its headquarters to the West Coast, and Union Carbide, the large chemical manufacturer that kept its headquarters in New York during the earlier exodus, just completed a move to Connecticut.

But there has been neither a wholesale shift of headquarters from Manhattan nor significant vacancies in midtown or downtown. Commercial rents, which climbed as high as $60 a square foot on the plushest parts of Park Avenue, are coming down slightly, according to Robert H. Mehlman, president of the commercial leasing division of the real estate firm Pearce, Urstadt, Mayer & Greer. But Mehlman said there has been no precipitous slide as there was in the mid-1970s.

The buildings that grace Madison Avenue, as well as many other midtown and downtown structures, are mostly leased before ground is broken.

"The outlook is grim," former deputy mayor Solomon says of the city's problems. "But that may be true everywhere, not just here."

Although New York may continue to lose lucrative manufacturing jobs, many of its key industries--such as advertising, banking, brokerage, communications, fashion, culture and transportation (a big proportion of Queens workers are employed at La Guardia and John F. Kennedy airports)--are unlikely to move.

In addition, said Chemical Bank's Spitznas, the support industries like accounting and law that many officials feared would follow coporate clients to the suburbs did not. Spitznas believes that the city's economic base is sounder than the doomsayers thought in 1975, when the collapse of New York was a topic on the nightly news and the butt of jokes on the talk shows.

Despite the new fiscal problems looming for the city, there is not as much concern about its ability to cope. For one thing, by 1975 several administrations had camouflaged deficits to pay current expenses--like taking out a second mortgage on a house to throw a banquet. The city's books were so snarled it took an accounting firm months to figure out how and where the city spent money. The city's economy was at its lowest point in decades.

Now the city's books are in order, and no administration can mask a deficit by borrowing from the future.

Furthermore, although the state watchdogs would rather the city had a consistent way of dealing with budget deficits, the 1983 deficit may be transitory--the delayed impact of the recession and decline in tourism on New York's tax receipts. Further, explains Chemical's Spitznas, the slowdown in inflation has a more immediate impact on revenues than on expenditures.

"Our problems are there," concedes Koch, but he claims they are manageable. When Koch became mayor in January 1978, he said, the city faced "problems that seemed unmanageable, undoable and unique. . . . Now our problems are exactly like those of other cities. We are no longer sui generis."

Koch said the city's fiscal house has been put in relative order. "There is fiscal stability even though there are money problems."

Rohatyn, who is head of the investment banking firm Lazard Freres, worries that the Reagan budget cuts will cause serious social unrest. But, he said, New York is "probably in as good a shape to face that squeeze" because it has been there before and has the facilities to cope with budget problems.

"We'll have problems, but we'll be able to identify them," he said.