Political power: two big-city mayors jockey to get it and keep it. Challengers face uphill battle against N.Y.C.'s Ed Koch

It's the summertime scramble to see who will lead America's largest city for the next four years. Carol Bellamy, currently the City Council president, shakes hands with people at the end of the day at an express bus stop in midtown Manhattan.

State Assemblyman Herman D. Farrell comes right to the phone when a reporter calls with a request for an interview.

And Edward I. Koch just remains what he is -- mayor and news-media star in this city of bright lights. He has the natural advantage of an incumbent, but he is also one of the few politicians around the nation whose face appears on post cards, book covers, and an off-Broadway play billboard.

These are the top mayoral contenders in the Sept. 10 Democratic primary. The winner will take on the Republican candidate, Diane McGrath, in November, though the Democratic contender usually goes on to become mayor.

Mayor Koch has been called a New Yorker's New Yorker -- combative, self-confident, known for chutzpah rather than charisma. His campaign has been marked with restraint, emphasizing how well the city has recovered from the financial crisis that he inherited when he took office eight years ago. There is little of the ``How'm I doing?'' showmanship that has marked previous campaigns.

Koch's television ads do not even feature the mayor until the closing seconds, when a small still shot of him appears in a lower corner.

But critics accuse Koch of ``hiding out'' to avoid the issues and to avoid giving his opponents free publicity.

While the mayor touts the city's economic recovery, Ms. Bellamy charges that he tends to react to crisis rather than to follow through with long-term planning for New York City. She says Koch is not doing a good job with mass transit, public education, housing, and crime. And she has begun to outline her proposals in campaign-issues papers, the first one on reducing crime and improving the police department.

Mr. Farrell, who is black, is the surprise result of an effort by minorities to oust Koch. So far, Farrell's support in both the black and Hispanic communities has been far from monolithic.

In his campaign stops, Farrell talks about the displaced and disadvantaged -- the homeless, the people caught in New York's housing bind, the children who need a better education, the elderly who are victims of crime.

A New York Times/WCBS-TV poll in May showed the mayor 50 percentage points ahead of Bellamy, with Farrell even further behind.

Indeed, both Bellamy and Farrell have had a hard time capturing the attention of New York City's nearly 2.5 million registered voters.

They also fall behind the mayor on large campaign contributions. According to recent financial disclosures, Bellamy has raised $615,000 compared with more than $5 million in Koch's campaign chest. Farrell has raised about $111,000.

Bellamy has consistently tried to make the race a two-person contest, and last week she filed a challenge in court over the legality of signatures gathered by Farrell.

But Farrell insists his campaign is doing well, despite challenges from Bellamy.

``The line [from potential voters] is that `We've got to rid of [Koch],' '' Farrell says.

Bellamy's campaign manager, Edward C. Wallace, says the battle is still uphill, but that her campaign is going reasonably well. The large number of volunteers and recent endorsements, including those of 32 labor leaders and of US Rep. Major R. Owens (D) of Brooklyn, are good signs, Mr. Wallace says.

One of Bellamy's strategies is to point out that though New Yorkers like the mayor's outspokenness, few believe he can solve pressing problems the city faces today.

``His popularity is mainly mouth-related,'' Wallace says of Koch. He adds that this is sometimes good, such as during the fiscal crisis when Koch's ``cheerleading'' galvanized the city. Even so, the mayor should be held accountable for the poor state of the transit system, public education, and housing, he says.

To bring this point home, Bellamy supporters have been putting up stickers that say, ``Do something about this'' on potholes, broken-down subway trains, and abandoned lots.

But there are plenty of Koch supporters.

``I'll vote for Koch,'' says Stan Levitsky of Queens, interviewed at an Upper West Side restaurant. ``He gets things done.''

Ruth Rand of Manhattan is a volunteer for Koch. She says there is a lot to be done in the city, ``and [Koch] is doing a lot of it.''

``You see how the economy is going and vote for the best person,'' says Thomas Lernihan, another Koch volunteer and a construction worker from Queens.