The Republican presidential contest moved south tonight, with John B. Connally accusing George Bush of being a liberal and Ronald Reagan of being inadequately trained for the presidency, and Reagan saying Connally, as usual, was about half-right.

Sen. Howard H. Baker Jr., the fourth man in a televised 90-minute debate here tonight, was content to keep alive his feud with Bush over his exclusion from last Saturday's Nashua, N.H., Reagan-Bush debate. Substantively, the fourth debate of the primary season produced so little disagreement that Baker commented at one point that "we really are all saying the same thing."

The format tonight, unlike other debates, allowed follow-up questions.

Bush, for example, was asked why people think he is fuzzy on issues; Connally, why his campaign doesn't appear to be going anywhere; Baker, how could he expect to organize an administration when his campaign has been plagued by mismanagement and poor organization.

But, overall, this debate probably helped Reagan consolidate the favorite's position he holds in the March 8 South Carolina Republican primary and the March 11 contests in Alabama, Florida and Georgia, by pitting Connally against Bush on a variety of issues -- including a charge of dirty politics in seeking black votes -- while leaving Reagan above the fray.

Connally, who has pinned his hopes for finally starting his becalmed campaign on his showing in this state, was considerably more aggressive tonight than he had been in Iowa or New Hampshire.

He said Reagan, the favorite in all four of the Dixie primaries after his landslide victory Tuesday in New Hampshire, had been a good governor of California, but "he's never been in Washington and has no experience in foreign affairs."

When Reagan rather mildly opened the subject of Bush's "liberalism" by saying the former ambassador "has more faith in big government than I do," Connally seized the opening to blast away at his fellow Texan.

"All the liberals apparently think he [Bush] is a liberal, because they're all for him," Connally said.

Bush made no direct response to the potentially damaging charge in this conservative state, and found himself more on the defensive than did any of the other candidates.

Responding to fresh complaints from Baker about Bush's role in keeping Baker and three others from participating in the Reagan-Bush debate Saturday in Nashua, Bush acknowledged that he had made a tactical error and wanted "to forget it."

Comparing the incident to being shot down as a Navy flier during World War II, Bush said ruefully, "The landing in the shark-infested waters of the South Pacific was a lot softer."

Baker said he was willing to let bygones by bygones, but only after taking considerably time to make sure that the South Carolina audience knew what had happened in Nashua.

Reagan, in his restored role as front-runner, managed to underscore his conservative credentials by condemning the use of marijuana and leading off what turned out to be a unanimous show of support for state "right-to-work" laws.

He rebutted the only serious criticism of him, Connally's claim that he lacked proper training for the presidency, by asserting that the California governorship he held for eight years was "the second-ranking executive job in the country."

Reagan was the innocent bystander as Bush and Connally, each anxious to close the gap on Reagan, exchanged bitter charges on their efforts to win support of black voters.

South Carolina's open primary law permits even registered Democrats to vote for Republican candidates, and tonight all four contenders asserted they were eager for black support and entitled to it by their records.

Reagan and Connally said they had appointed more blacks to office than had any previous governors of California and Texas, respectively, and Baker and Bush said they had supported civil rights legislation in Congress at a time in the 1960s when that was risky politics in their states of Tennessee and Texas.

But Connally rejected published charges that his organization had offered $70,000 to black leaders in return for their support, and Bush conceded that he had no evidence to support the charge, which Connally said originated in the Bush camp.

James Timmons Jr., a Bush campaign aide, had issued a press statement earlier in the day, charging that Connally had made a deal with black ministers to deliver 100,000 black votes in exchange for $70,000 in "walking around" money and the promise of donations to Allen University, a private black college.

"The Connally campaign effort to work black magic and to save his spiraling campaign here will fail blacks have no valid reason to support him or Ronald Reagan," the statement said.

After tonight's debate, Connally said Timmons had sounded out Connally co-chairman Gay Suber about obtaining "walking around" money and had been rebuffed. Connally identified Timmons as an aide to Harry Dent, a leader of the Bush campaign and a onetime official in the Nixon White House. Dent "is the original dirty-tricks man," Connally told reporters.

Dent, in an interview tonight, said he approved Timmons issuing the statement, and said that Bush is scheduling a meeting with black leaders next week. He denied Connally's personal attack.

Substantively, only one new issue was raised in the debate -- the question of nuclear waste disposal.

All four of the Republicans advocate nuclear power, but Reagan was criticized by the other three for saying that the problem of handling the radioactive leftovers should be left to private industry to solve.

Connally, Baker and Bush said the federal government should take the lead in formulating a waste-disposal policy in consultation with the states, but without an absolute veto-power by the states of nuclear-dump sites.

The debate had only four participants because Reps. John B. Anderson and Philip M. Crane of Illinois have not filed in South Carolina and Sen. Bob Dole of Kansas withdrew from the debate Wednesday as part of his shutdown of his presidential campaign.

The debate was carried live on public television, but the size of the audience may have been reduced by competition from an Atlantic Coast Conference basketball tournament game involving Clemson University.