AT a time when city leaders around the United States are struggling with lean budgets and growing urban problems, Boston Mayor Raymond Flynn keeps on working hard and winning elections. Seeking a third four-year term, the Democratic mayor won a landslide victory in Tuesday's mayoral election, capturing 75 percent of the vote.Challenger Edward Doherty, also a Democrat and president of the Boston Teacher's Union, ran a low-key campaign with a limited budget. During a time of declining city revenues, high unemployment, and increasing concern about public safety, Mayor Flynn showed that he still enjoys a strong base of support. "These are very tough times," he said in his victory speech. "We're seeing it all across this state, all across this country. This is not exactly the best time to be an incumbent politician in America." Some observers suggest that the third-term election victory will help Flynn gain national recognition; there has been talk that Flynn, now serving as president of the US Conference of Mayors, would make a strong vice-presidential candidate. But his general popularity at the local level was not surprising. In the city's September preliminary election, Flynn overwhelmed his two challengers, with 67 percent of the vote. In that contest, Flynn ran against Mr. Doherty and a black community activist, the Rev. Graylan Ellis-Hagler, beating both challengers in their own home precincts. In what he called a "grass roots" campaign, Flynn used no television or radio ads. He touted his success in keeping keeping the city's budgets balanced and maintaining strong ties to city neighborhoods. "He has a kind of stature because he's perceived as being able to put together this biracial, urban populist coalition which is very impressive, and he's done it in the face of a deteriorating economy," says William Schneider, a visiting professor of political science at Boston College. Political observers say Doherty, on the other hand, ran a remarkably passive campaign. A former Boston teacher, Doherty stressed improving public schools, encouraging economic development, and reforming the city's controversial police department. Doherty says his intent from the beginning was to run a clean, issue-oriented campaign. But he says he found Flynn's "strategy of avoidance" frustrating. Observers say Flynn's third term may well be his most challenging with a sour regional economy, a troubled urban school system, and a controversial city police department. The school system has been criticized for wasteful spending and bad management. Flynn was instrumental in pushing forward a new seven-member school committee, to be appointed by the mayor this January. The current 13-member elected committee will be abolished. Some political observers wonder if Flynn will be able to sustain his strong local base of support for another term while attending to his duties as president of the US Conference of Mayors. Joseph Slavet, a senior fellow at the John W. McCormack Institute of Public Affairs at the University of Massachusetts in Boston, says: "It's likely to be a mixture of boredom and outside interests that may take his focus away from the job to which he was elected."