The migrants who have made Houston one of the fastest-growing major cities in the United States are being felt for the first time in local politics in the mayoral campaign that will conclude Tuesday.

City Controller Kathy Whitmire, 35, is now clearly favored to defeat Harris County Sheriff Jack Heard, 63, in a runoff election Tuesday and in the process usher in a new era in Houston politics.

"There is a real growing feeling here of being on the brink of something new, of no more business as usual," said Clintine Cashion, Whitmire's campaign manager.

What this could mean for the city is the first serious attack on the side effects of growth that have made prosperous Houston an increasingly difficult city in which to live.

"Growth has provided opportunities," Whitmire said. "So from that standpoint it's been good. But at the same time, the failure of the city to provide services to keep up with it has hurt the quality of life."

Whitmire led a 15-person field with 36.5 percent in the first round of the voting Nov. 3. Heard was second with 25 percent, while Mayor Jim McConn, tarnished by personal problems and a deterioration of city services, ran a poor third in his bid for a third term. If elected, Whitmire would be Houston's first woman mayor.

With the likely election of Lance Lalor, a young city councilman, as city controller, leadership at City Hall would change sharply.

The diminutive Whitmire is an articulate accountant who earned a reputation for fiscal conservatism during her four years as city controller.

She has capitalized on the widespread frustration here with monumental traffic jams, run-down streets, poor garbage pickup and the breakdown of other services by pledging to improve the management of City Hall without tampering with the growth ethic here.

These issues are on the minds of many of the people who have come to Houston in recent years and are alarmed at how the city works. They expect action from City Hall, and Whitmire has become their candidate. Polls taken during the general election campaign showed that residents who had arrived in Houston since 1975 overwhelmingly supported Whitmire, while residents who arrived here before 1960 were more evenly split between Whitmire and Heard.

Richard Murray, a political scientist at the University of Houston, said newcomers, many of them young, well-educated professionals, support Whitmire because they identify with her.

"They're a helluva lot more like Kathy than they are like Heard," he said.

Heard, a big, bluff politician, is a throwback to the old Houston who is not likely to rock the boat at City Hall. He lacks Whitmire's knowledge of city issues and tried to build his campaign around rising fear of crime and his more extensive experience in local politics.

"The two things that show up in the polls are crime and leadership at City Hall," he said.

Heard has spent a lifetime in law enforcement, as a cop on the beat, police chief at 35, second-in-command at the Texas Department of Corrections for more than a decade and most recently sheriff of Harris County, which encompasses Houston. But he was hurt badly during the rough general election campaign by his inability to address other issues and has been a less formidable opponent for Whitmire than some strategists had predicted six weeks ago.

Newcomers are not yet active enough in local politics to guarantee a candidate's election, but Whitmire has put together a coalition that is unique here. It combines conservative Republicans, Democrats and minorities. Conservatives like her penny-pinching ways, liberals her background in Democratic politics and her positions on various social issues. She ran well in the general election among blacks and Hispanics and is expected to enlarge her vote Tuesday.

Whitmire's support differs in one important respect from that of former mayor Fred Hofheinz, a young liberal Democrat who served in the mid-1970s. Almost 60 percent of his support was from blacks and Hispanics, while Whitmire has strong support from whites as well. "She has a much larger base of support," Murray said.

Houston's Gay Political Caucus, a growing power in city elections, has endorsed Whitmire, and she has been aided by an army of volunteers who helped her overcome a lack of money during the general election.

"In the first election, the lack of money made us better because we knew we had to utilize the people we had," Cashion said.

Money has turned out not to be a problem in the runoff, as various members of the Houston downtown establishment, who supported McConn during the first round of voting, have begun to buy into the Whitmire campaign. Among her contributors in recent days are George Brown of Brown and Root, Inc., the giant engineering and construction firm, and several of the city's leading developers.

"Running for office in Houston is weird," Cashion said. "It's incredible the money that's rolled in in the last two weeks."