Voters here have been shaking their heads and derisively murmuring things like "only in Louisiana" and "Mardi Gras politics."

The object of their ridicule is the battle for the state's traditionally Democratic First District congressional seat - a bizzare and complicated contest that could give the district its first Republican representative in 103 years.

Even a strong Democrat like Allen J. Tillery, a popular lawyer who filed to run for the scat and then withdrew, says he wouldn't mind having a "good Republican" in office. Tillery said he would prefer anything to the current state of affairs, marked by the resignation of Democratic Rep. Richard A. Tonry under charges of vote fraud, federal indictments for illegal campaign financing, an exodus from the Democratic Party led by the man who accused Tonry of vote fraud, racial politics and the unfavorable national publicity generated by those events.

"All of this is kind of humiliating," said Tillery. "There is no dignity, no honor in all of this. And what is basic to this whole issue of who will represent us is dignity and honor."

Tillery, who said he withdrew from the special June 25 Democratic primary because he was neither the money nor the time to put together an effective campaign, added: "You might not have always agreed with old Eddie Hebert. He certainly had his ideas about things. But whatever your disagreements with him, you could never accuse him of serving without dignity and honor."

The reference was to F. Edward Hebert, formerly the conservative dean of the Louisiana congressional delegation and chairman of the House Armed Services Committee who represented the First District since 1940. Hebert's resignation last term allowed the current political struggle to take place.

It has been nasty.

Tonry, for example, defeated former New Orleans City Councilman James A. Moreau by 184 votes in the district's Democratic primary runoff Oct. 2. Moreau immediately began a legal campaign to overturn the election on charges of "widespread vote fraud."

Tonry, meanwhile, went on to defeat Republican lawyer Robert L. Livingston by 4,973 votes in the Nov. 2 general race.

But Moreau's legal struggle, taken up by a Republican U.S. attorney here who obtained fraud convictions on 20 Tonry supporters, led to Tonry's May 4 resignation, the first ever of a member of the House for reasons of primary election fraud.

Tonry, 42, and Moreau, 63, are running again - but not against one another, at least at first. Moreau switched parties recently and will run in the June 25 Republican primary against Livingston, the favored candidate, who is receiving support from the national party.

Also on June 25, Tonry will face 26-year-old state Rep. Ron Faucheux, who is called a "progressive-liberal" by his backers. Faucheux favors - among other things - zero-based budgeting, tough pollution controls and equal rights for women and minorities.

A third Democratic candidate, Florence Tye Gennison, is not expected to be a factor in the race.

Moreau and Livingston were supported in their races against Tonry by the powerful Plaquemines Parish (county) Democratic machine run by the heirs of the late, avowedly segregationist Judge Leander Perez. Moreau also received thousands of dollars' worth of free research and legal assistance from Perez' associates in his battle to unseat Tonry on the vote fraud charges, which have been unheld by a state court.

But now, it is not publicly known who, if anyone, the Perezes will support. They aren't saying. What political sources here say privately is that the Perezes have little interest in backing Moreau now because during the development of the Tonry scandal, Moreau's backers also were accused of stealing votes.

The 11-count indictment on charges related to illegal campaign financing was brought against Tonry by the same U.S. Attorney Gerald J. Gallinghouse; who investigated Tonry supporters on the vote fraud allegations.

Tonry, who was elected with strong black support is viewed here as a liberal. Some people, citing his opposition to increased defense spending (far different from positions taken by the hawkish Hebert, a close friend of the Perezes), call him a radical. At any rate, sources here are convinced the Perezes didn't like Tonry and that they used Moreau to get him out of office.

Leaders of the Perez organization could not be reached for comment. Moreau denied the charges that he was used, but acknowledged the ironics in the Perezes no longer being interested in him because of the publicity generated in the case.

"To the Perezes, politics is a way of life," Moreau said. "It's important to their survival and to the survival of their people in Plaquemines. I could appreciate whatever they do. If they feel that this seven-month legal fight with Tonry has hurt me, I could see them going with another candidate."

Moreau insisted that his surprise switch to the Republican Party was promped more by his adherence to conservative politics as espoused by the GOP than by pique at his Democratic former patrons. But when he announced his decision to switch, he also asked all of his Democratic supporters to switch with him. About 2,000 of them in his home base of Orleans Parish did.

By the may 25 party registration deadline, 3,600 First District Democrats had changed their registrations to Republican. However, not all of the changes could be attributed to Moreau, because Livingston had been making similar appeals.

Livingston, a 34-year-old former assistant U.S. attorney who describes himself as a "fiscal conservative," is quietly overjoyed by the turn of events.

He has been trying for 10 years to build up GOP registration in the First District, where 8,289 of the 215,000 voters were registered as GOP members in the Nov. 2 general election. Livingston received 56,679 votes in that race; Tonry received 61,652.

The upcoming GOP primary will be the first in living memory here. Never before was the Republican nomination considered important enough to be contested.

"We take the position that we welcome Jimmy Moau and his backers into the party," Livingston said. "I'd be the world's biggest hypocrite if I didn't say I'm glad Jimmy joined . . . Of course, I didn't expect him to join the way he did."

Livingston said he expects to beat Moreau "and when I do, I hope he will support me," Moreau has said he will if he loses.

Livingston refused to speculate on who his opponent in the Aug. 27 general election might be, should he, as expected, win the primary.

"I'm running as the best candidate rather than as the Republican candidate. This isn't really a race between a Republican and a Democrat," he said.

Livingston is given an excellent chance of winning a rematch against Tonry, whose federal trial on the illegal campaign-finance-related charges is to begin nearly two weeks after the primary. And he is given a good chance of beating Faucheaux, who at this point does not have much name recognition despite his reputation as a media-wise candidate.

The Republican candidate hopes to bolster his victory chances by going after the district's important black vote, which comprises 24 per cent of the total. He is being helped in that task by the Columbus, Ga., political consulting firm of Wright-McNeill and Associates, which has been hired for him by the Republican National Committee. Livingston unabashedly admits that the national party sees his campaign as a chance to broaden the GOP's base.

He claims his support from the Perezes, who are anathema to many of the district's blacks, was unsolicited and came only three days before the Nov. 2 election. He said he does not believe that support, or the absence of it, will hurt him in the current race.

But mostly, despite his claim that he is not running as a Republican, Livingston and his supporters are aware that they could be the chief beneficiaries of the voter resentment generated by the Democratic squabble.

Political observers here agree. "People are weary of Tonry and Moreau," said one knowledgeable Democratic politican. "There is no doubt about it that Livingston could pull this election out . . . the district may very well look to a Republican this year."