Seven years ago a young building contractor borrowed $1,000 from his mother-in-law, moved from a suburban apartment to the Cleveland neighborhood where he had gone to high school, and started fixing up a dilapidated old house.

Now the contractor, 32-year-old William T. Sullivan, represents his near West Side neighborhood on Cleveland's City Council and notes proudly that in the last 10 years private investors have spent $25 million in his area and renovated 500 houses.

Bill Sullivan is an urban phenomenon - the kind that newspapers write about and neighborhood groups boast - a suburbanite who has come back to the city.

The question is whether he represents a trend. Has the generation of movement out of cities and into suburbs ended at last? Is there a certifiable population flow back to the city? Are we on the verge of a new golden age for urban America in which the middle class and the tax base will be restored to central cities?

The answer to the first two questions is, probably not. Census statistics and other studies show that the old trends are continuing. The answer to the last question, however, is perhaps.

John F. Long, chief of the Census Bureau's population projections branch, says flatly, "There does not seem to be a movement back to central cities."

In a study for The Washington Post, Long looked at the nation's 153 cities with populations exceeding 100,000. He found that, generally, the bigger they were, the faster they declined between 1970 and 1975.

Of the six cities with more than 1 million population (New York, Chicago, Los Angeles, Philadelphia, Detroit and Houston), only Houston grew faster than the national rate of 4.8 percent in the five years. "And that was bcause it annexed many of its suburbs," Long said.

Of 20 cities between 500,000 and 1 million populations, only four - Phoenix, Jacksonville, San Antonio and San Diego - grew at a faster pace than the country as a whole.

Long found that 88 of the 153 cities lost population. Of the 65 that grew, 45 gained more than 4.8 percent by mid-decade.

"Still, you cannot say that the growth of the 45 cities represents a back-to-the-ctiy trend," he said. "Those cities, mostly in the South and West, never had a loss. They haven't had a downturn to come back from."

Overall, Long found that in the five-year period central cities over 1 million declined 5.4 percent, those between 500,000 and 1 million declined 500,000 declined 2.4 percent, and those between 10,000 and 250,000 grew 1.4 percent.

Some urban boosters question the importance of the census figures, noting that they cannot measure what has been happening in the last year or two.

"Something definitely is going on," says housing consultant Nathaniel H. Rogg. "When you walk the streets of cities, you see it."

I've lived on Q Street off 77th since 1963. The guy next door paid $42,000 for his house in 1970. He sold it in March for $170,000. Now is that just inflation.

"Look at Logan Circle, Shaw, Capitol Hill, Adams Morgan. Everyone I've met is enthusiastic as hell about the city, and it's happening all over the country. There are a lot of indicators but no statistics. I think the gross figures are almost irrelevant."

Rogg, for years executive vice president of the National Association of Home Builders, concluded in a 1977 study of housing rehabilitation in 11 cities that "a trend of decline . . . has not only been slowed but in many cases has been arrested.

Others have noticed similar signs.

The Urban Land Research Foundation here points to the zooming real estate prices in the Victorian Crescent that wraps around downtown San Francisco. There, in the Haight-Fillmore and Hayes Valley areas, young professional people, many of them homosexuals, are moving in and restoring old frame houses.

Even in Detroit - long a national symbol of fear-ridden demoralized cities - housing prices, which have skidded steadily for years, have bounced back in certain parts of town, says realtor Roger H. Blackwood.

In Baltimore, realtor James P. O'Conor says some of his suburban neighbors are fascinated by the rejuvenation of such city areas as Charles Village, Patterson Park, Otterbein and Fells Point.

"Now they're saying they plan to move back to town as soon as their children leave home," O'Conor reports, "They never would have said that a few years ago."

Whether suburbanites are moving or will move back to cities is, at least, questionable.

Duane McGough, who heads the division that analyzes housing and demographic trends at the Department, says, "No one has found evidence of a reversal of the general trend out of cities."

A HUD study concluded in May by housing consultant Kathryn P. Nelson looked at 11 metropolitan areas and found that, as of mid-decade, the number of people returning to the city "was small in magnitude and did not represent much of a departure from past tendencies toward decentralization.

Nelson said there is some evidence of a small net influx of whites into Los Angeles. Census Bureau experts say they are mostly Hispanics moving to such areas as the San Fernando Valley, not the central part of the city.

In the other 10 metropolitan areas studied - Washington, Atlanta, Philadelphia, Detroit, Newark, Chicago, Boston, Pittsburgh, New Orleans and Dallas - Nelson found that, as of 1975, "whites still appear to avoid the central city."

She noted that Washington, D.C., officials have said that for the first time in 25 years this city had a net increase in its white population - that between mid-1975 and mid-1976 the white total grew from 162,700 to 169,100, from 22.5 to 12.9 percent of the total population.

But Nelson questioned whether Washington, with its high proportion of single people and its magnetic pull of white-collar government jobs, is typical of central cities.

She also found that in five metropolitan areas - Washington, Newark, Los Angeles, Philadelphia and Atlanta - there were "marked increases" in the rate of blacks moving to suburbs and in their proportion of the suburban population. Yet in the other six areas studied, the black "outmovement" was swamped by that of whites.

Among whites, she found that those aged 20 to 34 are increasingly attracted to cities, especially in Washington and Atlanta.

But she concluded from an overall look at national population and housing surveys between 1970 and 1976 that while more blacks are choosing suburbs than in the past, a majority are still going to cities and that there is "little evidence of increased white movement toward cities."

"Instead, complete data on both inmigration and out-migration for central cities, suburbs and nonmetropolitan areas demonstrate that white migration since 1970 continued to be effectively directed from central cities into suburbs and, increasingly, into nonmetropolitan areas," she said.

For cities there is good news and bad news affecting prospects for future growth.

The bad news is that many economic expect a continued job drain in [WORDS ILLEGIBLE] although some say President Carter'sprograms to concentrate [WORD ILLEGIBLE] construction and procuremed in cities and his proposals to induce business to hire the longterm unemployed may help.

"For most cities the recent trend clearly indicate a general shrinkage in overall economic activity in the foreseeable future," according to a new report by J. Thomas Black of the Urban Land Institute, a nonprofit research organization here.

Black, however, does not think cities "will become completely dysfunctional." They will still retain many manufacturing plants that need their existing rail and waterfront locations, he writes, adding:

"The key to economic viability for most cities will lie in the service sector" - transportation, communication, finance, insurance, real estate, business services like accounting, health and education - which has expanded in most cities.

School busing is another factor in urban population loss, says David Armor, a sociologist at the Rand Corp., a Santa Monica, Calif., think tank.

In a recent study of 54 school districts, Armor found widespread white flight in 23 cities that had more than a 20 percent minority enrollment in public schools plus easily accessible suburbs.

"In a geographically small place like Boston, which has both working-class and high-economic suburbs, two-thirds of the whites fleeing busing went outside the city," Armor said. "In a big place like Louisville-Jefferson County, the flight was not so visible. Two-thirds went to private schools; one-third migrated."

Armor said his interview showed racism was a factor in the white flight, "but there were also strong feelings against being told where to go - they didn't want their kids going to alien neighborhoods even if they were white neighborhoods.

"Busing adds another burden to a city trying to maintain its middle-class population, including blacks, who also flee from busing, but especially whites. As long as busing is around, the city is going to be unattractive to the white middle class."

Some urban optimists think that good news for the cities lies in the rising cost of energy. If nothing else, they say, high energy prices will drive suburbanites back.

But Ellis Cose, a senior fellow at the minority-oriented Joint Center for Political Studies here, argues against that possibility.

He notes that people were driven out of the cities for a variety of reasons - educational problems, violent crime and a desire for a better quality of life among them - and, he says, high energy prices will not necessarily drive them back.

Contrary to popular thinking, Cose says, most suburbanities do not work in cities. Two-thirds work in suburbs.

"It is obvious, then, that even if higher gasoline prices did cause most suburbanites to consider moving closer to work, it would not cause them to consider moving to the city," he wrote in a study entitled "Energy and the Urban Crisis."

Indeed, "the continuing trend of jobs opening up in suburban malls as jobs close down in the cities might well serve to nudge the average suburban work-trip distance down," he said.

To the argument that utility costs are higher in single-family detached homes than in apartments, Cose replies that "the average person would not necessarily give up the suburbs to move into an apartment in the city."

As for new forms of energy, such as solar heating, Cose says they are equally available to the suburbs and may do nothing more than encourage the growth of more apartments and town houses there.

Nevertheless, there are some positive signs for cities. One is that the rate of migration from at least some of them is slowing down.

Census Bureau demographer Mary Kay Healy said that in Philadelphia, for instance, migration from the city averaged 2.5 percent a year for the first three years of the decade; now it is 1.5 percent. For Chicago the rate was 3.5 percent; now it is 2.6. And some cities, such as New Orleans and Seattle, showed population gains from 1975 to 1976, reversing five years of decline.

"Maybe all the people who were going to leave have already left," Healey said.

Another sign of rejuvenation is that in many neighborhoods of many cities the middle class is moving in and fixing up.

Although in some cases they are driving out poorer, older residents and thus creating additional problems for mayors, in the long run, according to some experts, the middle-class urban pioneers represent last-chance hope of cities and their sagging economics.

Kenneth T. Rosen, an urban economist at Princeton, says that overwhelmingly these new city investors are young people buying houses in the city where they already live.

In a study of the nation's 22 largest cities, Rosen has found that "nearly 80 percent of the new investors lived in other neighborhoods of the same city, and of those, 91 percent were renters."

"Mostly they're the 'baby boom' generation, kids born between 1947 and 1957, and they're now forming families and buying their first house," he said,

"Since housing costs in the suburbs are going up at a faster rate, cities are getting more attractive - at least to the younger people."

In terms of money, the central-city homeowners are outpacing their suburban counterparts. An Urban Institute study by former senior reinvestment - the amount spent on home renovation, repair and maintenance - is growing faster in central cities than in the nation generally.

In 1970 the national total was $9.5 billion; in 1971 it was $10.2 billion and in 1975 it reached $15.4 billion. For cities the total in 1970 was $2.096 billion; it slipped to $2.079 billion the next year, but by 1975 it was $4.135 billion - nearly double, while the national increase was about 62 percent.

"We keep hearing the horror stories about cities, but there is a counter-trend in certain parts of them," says Bob Kuttner, executive director of the federally funded National Commission of Neighborhoods.

"Whether it continues is not clear. But there's great hope in one statistic: the number of people reaching the age of forming families and buying homes in the 1980s will be 50 percent higher than it was in the 1960s.