As the Democratic Party is moving to the right and labor unions, blacks and the poor have fallen out of political fashion, a fascinating experiment is taking place in George Wallace country.

Lt. Gov. Bill Baxley, one of four candidates in the June 3 Democratic primary and the leading contender to succeed Wallace as governor, is defying conventional wisdom by running as a liberal. He is embracing labor unions and blacks; defending school teachers from attack, and promising to spend more money on day-care centers, schools and senior citizens' programs.

Such moves would be considered suicidal in most southern states, where political liberalism is shunned. But Alabama is different.

Alabama is the only heavily industrialized state in the South. "We've had big union factories for a long time," said Baxley, a controversial political figure here since 1970. It is also a state with a long tradition of populism, rooted in the Farmers Alliance organizing drives among independent white small farmers in the 1880s and 1890s.

A red-faced tobacco chewer with a booming voice and a thick accent, Baxley is using this populism to deflect charges that endorsements from the AFL-CIO, the Alabama Education Association, two influential black political organizations and the state's trial lawyers have made him "the special-interest candidate."

"The big boys who pull the strings are pouring money at us," Baxley says as he moves from one small rural town to another. "They're saying the white voters who supported George Wallace, the blacks, the teachers and the working people are all for Bill Baxley like that was something to be ashamed of," he bellowed from the courthouse steps here last week. "What in the world is wrong with that? Those are the average people I want to represent," he added.

George C. Wallace used the same populist appeal, combined with racism until recent years, to dominate Alabama politics for a quarter century. But Wallace, tearfully saying "I've climbed my last political mountain," announced this spring that he would not seek an unprecedented fifth term.

The major candidates in Tuesday's primary have shied away from directly attacking Wallace on the stump, but Wallace's shadow hangs heavy over the race.

"George Wallace was a masterful politician in the populist tradition," said former governor Fob James, who is trying to regain the post he won in 1978. "But nobody knows what these populists' instincts are anymore or how they'll sort out in this election."

Attorney General Charles Graddick, running as a "new face," and former lieutenant governor George McMillan, who narrowly lost to Wallace in the 1982 Democratic primary, are more implicit in their criticism.

Graddick argues, "It is time to change Alabama's image -- to make Alabama the comeback state." McMillan tells audiences, "A new day is dawning. This election is the most important one in Alabama history. We have the opportunity to replace one era of Alabama politics with another."

But with the election only days away, Baxley, who defends Wallace's record, holds a slim, but apparently widening lead in opinion polls and appears likely to capture one of the two slots in the June 24 runoff. One poll conducted by the Birmingham Post Herald showed Baxley supported by 43 percent of those approving of Wallace and attracting almost as many conservative as liberal voters.

Guy Hunt, a former Cullman County probate judge, is expected to defeat Birmingham businessman Doug Carter, a former Wallace speechwriter, in the Republican primary.

The contest for the second spot in the Democratic runoff has turned into a nasty fight.

When Wallace pulled out of the race in early April, James ranked No. 2 in polls. But Graddick, the only one of the major candidates who had never previously run for governor, quickly passed him by with a slick advertising campaign that charged "Fob James let convicted criminals go free" while governor.

James, whose administration was marked by political blunders and high unemployment, counterattacked as he fell behind in the polls.

In one widely aired television commercial, James, a former All-American halfback at Auburn University, shook his finger at the camera, accusing Graddick of misleading voters with a "deliberate lie, and you know it."

Graddick replied with a TV ad featuring one of the world's ugliest frogs. The frog jumped as an off-camera voice said, "When you remind Fob James of his record, he flips . . . . Now Fob James is calling Charlie Graddick a liar, which is like being called ugly by a frog. And those are the facts, warts and all."

Despite a last-minute advertising blitz by James, including an hourlong radio show broadcast each day, Graddick continued to rank second in polls and appeared headed for a the runoff.

This bothers Baxley, who fears Graddick may tear apart his loose coalition of blacks and white populists with "the nastiest runoff campaign in history."

A former Republican, Graddick, 41, is the only major Democratic candidate not to court black voters. He is best known for his tough law and order stance and his support for capital punishment. During his 1978 campaign for attorney general, he was quoted as saying that murderers should be "fried till their eyes pop out and smoke comes out their ears."

Elected attorney general in 1970, Baxley built a national reputation through his handling of several cases, including the prosecution of a Ku Klux Klansman for a 1963 Birmingham church bombing in which four black girls died. But he also has been embarrassed by newspaper stories about his drinking, gambling, financial dealings and alleged womanizing. In March, the Birmingham News reported that state police officers assigned to Baxley used state cars to transport a young woman reporter to and from his apartment late at night several times.

Baxley refuses to change his life style. "I don't want to be a hypocrite," he said in an interview. "I've been this way since I was 17 years old. I know politically I'd be better served not going out and having a good time. But I still have a life to lead. I'm not going to tailor it to something I'm not."

He knows his campaign defies conventional political wisdom, but Baxley claims Democrats around the country have misread the political tea leaves. "I've always felt people weren't rejecting the philosophy of the Democratic Party," he said. "What happened is Ronald Reagan is a champion communicator. People mistook the message for the messenger. Democrats just have to learn to communicate in a language people understand. You can't do it in a Jimmy Carter way. He was too soft."