On the November night in 1981 when Kathy Whitmire was elected the first woman mayor of Houston, a local political analyst offered a word of warning.

"Many of the traditional power brokers in the city that did not support Whitmire will have to be convinced that she can do a competent job as mayor or they're going to start looking for an attractive candidate to run against her in 1983," said University of Houston political scientist Richard Murray.

But Whitmire cruised through her first year, with nothing much more worrisome than wisecracks describing her as a look-alike for actor Dustin Hoffman in "Tootsie."

Now, however, a political challenge has arisen that suggests that Murray may have been right. After a year of accomplishment and seemingly still popular, Whitmire finds herself with two likely opponents for next November's election.

One is City Councilman Larry McKaskle, a pro-business Whitmire opponent. The other is Bill Wright, a Houston oilman and Democratic fund-raiser who was one of Whitmire's early supporters in 1981. Others are said to be considering the race.

The anticipated struggle is being watched with fascination and puzzlement by Houston business and political leaders, who say some members of the local establishment are trying to get Whitmire's attention because they believe she is ignoring them.

"There's a major power struggle going on in this town," said a city councilman. "The 1981 election changed a whole lot of things."

The election that brought the 5-foot-tall, 36-year-old accountant and former city controller to power was dramatic evidence that rapid growth and migration had changed the politics of the nation's fifth-largest city.

Whitmire first deposed vulnerable Mayor Jim McConn, who was supported, if not loved, by the establishment. Then she crushed Harris County Sheriff Jack Heard, a Houston good-old-boy, in the runoff.

Business leaders who had opposed Whitmire began paying their respects with hefty donations to her campaign fund. But Whitmire made few direct overtures to them.

"She doesn't seem to trust the establishment," one businessman said.

Instead, she set out to fulfill her campaign promises.

"I put my priority on managing this large, billion-dollar operation with 20,000 employes, and it doesn't leave a lot of time for handshaking and backslapping and making people feel comfortable and happy about me personally," she said in an interview. "But it's my belief that I can deliver the product."

Candidate Whitmire pledged to bring sound management to City Hall, arguing that fiscal restraint and bureaucratic reforms could overcome growing traffic congestion, inadequate mass transit, rising crime and declining city services.

Once elected, Whitmire reorganized the mayor's office to eliminate what she considered special-interest pleading. She changed the fiscal year and instituted procedures that gave the city its first on-time budget that anyone can remember.

She hired Atlanta public safety director Lee Brown as the city's first black police chief and recruited other talented people to handle transit, the municipal airport, personnel, finance and legal affairs.

During her first year bus service improved, plans for a subway system moved ahead rapidly, the City Council imposed the first limits on development and the mayor personally negotiated an agreement with police and firefighter unions to give city leaders more freedom to hire and fire top assistants in the two departments.

It was an impressive performance, and a poll taken by Murray last November showed that the public approved of Whitmire by a 2-to-1 ratio.

"I think she is moving the city in the direction it ought to go," said city Controller Lance Lalor. "That's no small matter."

Whitmire's record won over some critics, but it apparently wasn't enough to satisfy others in the business community or some members of the City Council.

"There are a helluva lot of people who feel estranged from this administration," said a businessman who has been taking his own soundings.

Critics say Whitmire is inaccessible, inflexible and surrounded by protective and inexperienced aides. "She has an almost Richard Nixon dislike of the press," Murray said. In some respects the complaints are reminiscent of those once leveled at President Carter.

"She has focused pretty largely on being a manager," said a man considered her ally. "Her ultimate success is going to depend on how much she grows in that office and how much she expands her vision."

To Whitmire, process often has taken precedence over good politics, and she has devoted herself to changes that, while useful, have little appeal to the public at large. Along the way she has offended some powerful interests.

When she negotiated the civil services changes with the police and firefighter unions she apparently did so without informing members of a blue-ribbon committee she had appointed to help gear up for a citywide referendum on the subject. Many committee members, including some of the city's leading executives, said they felt betrayed when they learned about the deal in the newspapers.

"It was a mistake to assume what you came up with was more important than how you did it," said Jerry Wood, Whitmire's research director.

Lately, Controller Lalor has criticized Whitmire for ignoring warnings that the city faces a budgetary shortfall. And, recently, Whitmire bruised council members' feelings over the replacement for a councilman who died. She faces a possible tax increase this spring because of the sluggish economy, a fight over a new toll road favored by much of the business community and criticism that she isn't doing enough to attract business to the city.

Still, Whitmire is well-positioned politically, and Murray said he doubts she can be defeated next fall, partly because Houston voters rarely turn out a mayor after one term. But the challenges are important for what they may represent.

Wright's entry surprised Whitmire and many of his friends, who said recently that they could not understand the rationale for his candidacy.

Wright, charging that Whitmire had "lost control of the city," said he decided to run only at the urging of Walter Mischer, a local developer who is considered the most powerful behind-the-scenes operator in Houston.

Mischer, a key fund-raiser for former governor Bill Clements (R) and Sen. Lloyd Bentsen (D-Tex.), could not be reached for confirmation. Other sources said Wright had come to Mischer to say he was running and that Mischer had indicated that that was all right with him. They expect Mischer to give Whitmire at least token public support.

But Wright's candidacy is interpreted as evidence that some members of the business community, including Mischer, want to make the mayor more aware of their dissatisfaction, even if they are not loyal to Wright.

"They're saying, 'Let's bloody her up and really go after her in two years,' " one local politician said.

Whitmire, meanwhile, dismissed the challenges. Of Wright, she said, "It escapes me why he is running. He must have some other agenda." As for Councilman McKaskle, she said in a statement, "We will miss him."