Frances Bunton, age 63, was impressed with the smiling woman riding on the back of the silver convertible.

"She's got her feet on the ground," she said as the Sedgwick County Fair Parade passed by in the 96-degree sun. "She's got a nice personality; she doesn't try to promise too much. And she ought to have some knowledge, coming from a family of politicians like she does."

"I won't vote for her just because she's a woman though," Bunton added quickly. "I'm not a libber, don't you know."

Until a few months ago, Bunton and most everyone else in Kansas had never heard of Nancy Landon Kassebaum, the 46-year-old woman in the convertible. And few of those who had, took her candidacy for the U.S. Senate seriously.

She was known, even to friends and neighbors, only as a civic-minded, soft-spoken housewife, whose father had won the 1936 Republican nomination for president. She had, she says, devoted her life to her family. She'd married young, raised four children and built a life around her home.

Her only election to the school board in the town of Maize (Population 785); her only experience in Washington was a brief stint as a caseworker for Sen. James B. Pearson (R-Kan.)

But now she is going into Tuesday's primary election here as the favorite to win the Republican senatorial nomination over eight other opponents, including a cattle buyer who says "it's time to send an honest bull shipper to Washington."

Win or lose, her story is one of the most remarkable political tales in 1978. It is one that at once frustrates and baffles her opponents, many of whom have far better political credentials.

Much of her success has to do with her maiden name - Landon. For although her father, Alf Landon, failed even to carry Kansas, perhaps the most Republican state in the union, against Franklin Roosevelt in 1936, he is, at 91, regarded as the state's resident political sage.

"You just don't run against Alf Landon in Kansas. He's a living legend here," says one opponent, Samuel Hardage, a self-made 38-year-old Wichita millionaire. "If Nancy Kassebaum was running as Nancy Kassebaum she wouldn't even be in the race. It makes me think I should have changed my name to Samuel Ike Eisenhower Hardage.

There is some truth to what Hardage, who is considered one of the two other top contenders in the race, says. [WORD ILLEGIBLE] Nancy Landon Kassebaum, whose slogan is "a fresh voice, a trusted Kansas name," has used her family name and connections for all they are worth.

But that ignores the fact that she has but together an effective campaign and that her sincere, girl-next-door personality has somehow touched nerve endings at a time when traditional politicians are almost universally distrusted here. Her appeal touches men as much as women.

Stuart Awbrey, publisher of The Hutchinson News, put it best. "She gives the impression of being so naive at what she's doing that you want to go out your way to help her do it," he wrote in a column. "I don't say Nancy uses sex, or feminine wiles to be more polite about it, but it didn't sink in to me until some hours after our last visit that she had been feeding my ego rather than trying to push her own. I'm a pushover for that sort of thing."

Kassebaum's political career didn't begin until her marriage fell apart a few years ago. Until then, she says, "there was never a time in my life that I could have done this. My children (youngest is now in high school) were growing up. I've always been family oriented."

When she seperated from her husband, a wealthy lawyer who is working in her campaign, she took a job on Pearson's staff. When the senator, who was considered a shoo-in for reelection, abruptly announced he wouldn't seek another term last fall, his Senate seat went up for grabs.

Dr. Bill Roy, a popular former congressman who almost beat Sen. Robert Dole (R) in 1974, promptly jumped into the race on the Democratic side. He became the early favorite, raising the still very real possibility that Kansas might send a Democrat to the Senate for only the second time in its history.

Republicans, however, were in disarray. Kassebaum talked to some party leaders last December about the race but received little encouragement, even from her father. "People told me they didn't think Kansas was ready for a woman senator" she says. "They didn't think I was a serious candidate."

Kansas voters have elected a woman representative, Democrat Martha Keys, however.

By the time Kassebaum decided to run in March, the Republican field was already crowded. Six candidates, including Kassebaum, emerged as major contenders: state Sen. Jan Meyers; state Senate Majority Leader Norman Gaar; Deryl Schuster, a former Pearson aide and a former Small Business Administration office; Wayne Angell, a wealthy economist and former state legislator, and Hardage. Three others, including L.C. John Fitziarrel, the self-proclaimed "honest bull shipper" were given little chance of winning.

With that many candidates, one might think this would be one of the most exciting Senate races in the state's history. But voters have responded to it with a big yawn. And the only real issue to emerge among the Republicans has been "who could beat Bill Roy."

Relying chiefly on their own personal wealth, only three candidates - Hardage, who spent more than $300,000 of his own, Kassebaum, who spent $115,000, and Angell, who spent $140,000 - were able to mount major television advertising efforts. And when The Kansas City Times polled voters last week, it found 29 percent favored Kassebaum, 16 percent Angell, 10 percent Hardage and 8 percent Meyers. The other candidates were far behind.

However, 29 percent of those polled were undecided. "It all boils down to voter turnout," Hardage said Friday. "If it's a low turnout Angell or I will win. If it's a high turnout Nancy Kassebaum will win. It's still a horse-race."

Hardage mounted a highly professional, half-million-dollar campaign with a flock of outside experts, voice lessons in New York and direct mail. He even bought his own campaign airplane. He is clearly baffled by the Kassebaum phenomenon and how to deal with it.

"She's gotten through this whole thing unscathed," he complained in an interview. "How could a big 6-foot-4 football player like me attack that tiny nice lady and get away with it."

The other candidates apparently share his frustration. Much of it came out in the final television debate of the campaign, broadcast yesterday in Wichita.It was the first time Kassebaum had faced sustained attack.

Her opponents went after blood. Hardage questioned her stands on the Panama Canal treaties (she supports them) and legalized abortion (she's for it). Angell challenged the value of her experience in Washington as a Senate staff caseworker. And Gaar jokingly asked what she'd think if he changed his middle name to Eisenhower.

With election day so close, it's hard to estimate the impact of such attacks. But if nothing else, it may set the scene for a race this fall against Roy, who faces only weak opposition in the Democratic primary.