Everywhere he goes in this state where he's won election as a Democrat, an Independent, a Dixiecrat and a Republican, Strom Thurmond is introduced as "a legend in his own time."

At 77, he still has that rare peculiar magic few policians ever achieve. Teen-agers flock to his side for autographs. College girls fawn over him. And old men nod in agreement when his old friend, former governor James B. Edwards, declares, "If you can't trust Strom Thurmond, who can you trust?"

But Thurmond's popularity is being put to a severe test these days as he moves from the red hills of the Piedmont, across the piney wood foothills and into South Carolina's low countries stumping for his choice for the Republican presidential nomination -- John B. Connally of Texas.

Thurmond has pulled out all the stops for Connally. He's made television commericals. He's placed countless phone calls to the political cronies he has accumulated over the last 50 years. And the senator and his wife, Nancy are criss-crossing the state for Connally every chance they get.

But even Thurmond now concedes that Connally's once-promising chances of upseting Ronald Reagan in this state's March 8 GOP primary have almost disappeared. If he even finishes second, it will be remarkable, Thursmond said one day last week.

Other knowledgeable observers predict Connally will finish third. This could be devastating for the former Texas governor and Treasury secretary, whose campaign strategy has long hinged on a strong showing in the South.

"They way I look at it Connally has got to win here," says Lee Atwater, Reagan's state campaign coordinator. "If he can't win in South Carolina with an unlimited checkbook and the support of Strom Thurmond and Jim Edwards, where can he win?"

The South Carolina primary is the first Republican test below the Mason-Dixon Line, and its result is expected to have a psychological impact on primaries in Alabama, Florida and Georgia three days later.

Until about six weeks ago, it looked as if South Carolina would provide Connally with a one-on-one showdown with Reagan, a chance to pump new life into a sagging campaign. But GOP rivals George Bush and Sen. Howard H. Baker Jr. (R-Tenn.) made 11th-hour decisions to contest the primary.

With his upset victory over Reagan in the Iowa precinct caucuses, Bush, never considered a strong candidate in the South, suddenly became a force to be reckoned with.

"Connally was an alternative to Reagan here. Reagan was out front, but Connally was closing in on him," said Harry Dent, a lingtime Thurmond protege who has become Bush's chief South Carolina strategist. "After Iowa all that got cut in half. Now he [Connally] is throwing in the furniture and everything he's got to keep the old fire burning."

Polls taken by a Charleston newspaper and Reagan's polling firm lend credence to Dent's statements. They show Reagan as leader, with Bush ahead of Connally from three to six percentage points. In addition, Reagan won 52 percent of the vote, Bush 26 percent and Connally 15 percent in a straw poll taken last Monday at Republican precinct reorganization meetings in populous Richland County, where Columbia, the state capital, is located.

Dent, who is plugging Bush as a conservative among moderates and a civil rights advocate among blacks, says a strong Bush finish in New England primaries might have him enough momentum to beat Reagan here.

"It's going to be a real horse race," says Dent, a former Nixon White House political operative. "It's going to mean that Reagan is either going to get scared to death or get beaten in South Carolina. I don't think he can afford either."

Connally, however, may be the closest-watched candidate here. After his weak showings in Iowa and Arkansas, and with his fortunes not expected to improve in the New England primaries, his political survival will be at stake in the South.

The candidate dismisses such suggestions. "This is not Armageddon. I don't think it's Armageddon for me any more than for any of the other candidates," he told a news conference aboard the old aircraft carrier Yorktown, adding at another point, "I can run third in every state in the country between now and Detroit and still be in the race."

On paper, Connally looks formidable.His pragmatic conservatism, wavy silver mane and faint drawl would seem ideally suited to this state. His refusal to take federal matching funds makes him eligible to spend more money -- if he had it -- than any of his opponents, who are limited to spending $347,000 here.

He started compaigning early, and is spending more time (from 15 to 18 days between Oct. 8 and March 8) than any of his rivals. Bush has visited the state only once.

There is little doubt taht Reagan is by far the most popular candidate among Republicans. But this is the first presidential primary in state history, and although only GOP candidates will be on the ballot, Democrats, Independents and Republicans will be eligible to vote.

Then, there is the "Strom factor." After dominating state politics for 34 years, Thrumond is a folk hero in South Carolina, regardless of what he is thought of elsewhere.

At 77, he has the build of a high school athlete. He rises at 5:30 a.m. each day, does 30 minutes of calisthenics, lifts weights and heads out for a 2 1/2-mile run. His hair -- helped along by two well-placed transplants -- is a rusty orange; his back is ramrod straight.

His four children, all 8 and under, and his young wife make him an ageless wonder. When Frank Howard, a former football coach at Clemson University, joked, "This morning in Aiken at 3 o'clock Strom's third wife was born," the crowd roared with approval.

Thurmond's pitch for Connally is simple and direct. The one-time Democrat, he told more than a dozen audiences last week, is a "fellow Southerner, a patriot and a great American."

"I don't know any man on the political scene today who is more dynamic, more agressive and more forceful, who is as tough as this man, and we need a tough man."

Then Connally follows Thurmond to the podium, his message is a gloomy one. The country is going to the dogs, he says. President Carter's economic policies have been a disaster; his foreign policies have made the United States a laughing stock of the world.

The Carter administraton's current saber rattling is ill-conceived and fool-hardy. "We shouldn't be talking about war," he says. "We shouldn't be thinking about war. We should be talking in a very firm, calm voice while we build up our military."

Some who hear Connally love the message. "Think he's great. I wish he could go in there [the White House] tomorrow," E. A. Pollack, a retired four-star Marine general, said after hearing Connally speak at the Beaufort National Guard Armory last week.

But Thurmond is worried that not enough people will get a chance to hear Connally, and that Thurmond won't be able to help him enough. "A fellow can get votes for himself, but he can't always get votes for another man."