South Dakota, the state that gave the Democratic Party an antiwar presidential candidate in 1972, has three Vietnam Veterans running for the Senate this Year.

Two more Vietnam veterans, including one former prisoner of war, are running for one of the state's two congressional seats.

But if one is looking for some deep symbolic meaning in this, it isn't there.

"It's just our age. The three of us in the Senate race are all 35," says Don Barnett, former Rapid City mayor, who is seeking the Democratic senatorial nomination in Tuesday's primary.

"The war wasn't popular in South Dakota, but it sure wasn't like Madison, Wis., or any place like that. I didn't have any of my friends at South Dakota State University who avoided going into the army," he said.

There has never been a primary election here quite like this one, however. Both Republicans and Democrates consider this a watershed year, one that could set the tone in the political balance of power here for the next decade.

No incumbents are running for the three top seats up for grabs-the governorship, the U.S. Senate seat now held by the retiring Democrat James Abourezk, and one of the state's two congressional seats. So an unusual set of primary battles has developed with a cast of colorful candidates.

Take the Republican gubernatorial race, for example. It pits state Attorney General William Janklow, who takes his job so seriously that he sometimes takes to carrying a machine gun or pistol, against two state senators.

One , LeRoy Hoffman, is a former professional opera singer: the other, Clint Roberts, is a ruggedly handsome rancher who has appeared as a cow boy in TV commercials for Malboro cigarettes and Schlitz beer.

The Democtratic primary is just as crowded, if less eclectic. The early front-runner. Lt. Gov. Harvey Wollman, is being given a stiff challenge by state Sen. Roger McKellips, a smalltown banker and, like Hoffman, a millionaire, which in itself is an oddity in state politics here.

Traditionally, South Dakota is a bedrock Republican state. In the 34 years before 1970, it elected only one Democrat to Congress-Sen. George McGovern, the Democratic presidential nominee in 1972.

"South Dakota was such a Republican state that even people who were interested in the Democratic Party didn't want to let anyone know about it." his wife Eleanor, recalled here the other day. "We'd consider ourselves lucky if we got a dozen people together for a meeting. We had trouble filling slates even for statewide offices."

The Democratic Party, however, became respectable in the state during the 1960s, and made major inroads during the Nixon years. Today it controls the govenor's office and both Senate seats.

There is surprising agreement between both parties on what happened. "The Republicans had things their way so long they took elections for granted," says Norma Brick, executive director of the state Democratic Central Committee. "They got awfully lazy. They didn't do much work. They didn't raise much money. But now that's changed."

The Republican Party has rebounded during the last two elections, and this year is hoping to reestablish itself as the state's dominant party.

Meanwhile, Democrats suffered two major blows. First, Abourezk decided not to run for a second term. Then, Richard Kneip, who had served eight years as governor, announced he was bowing out of elected office.He has since been appointed ambassador to Singapore.

This threw both the Senate and governor's races wide open. And when Rep. Larry Pressler, the young Vietnam veteran and former Rhodes scholar, decided to seek a Republican sensatorial nomination, his congressional seat also opened up.

"This year will determine the direction of South Dakota politics for a long time," say Democratic senatorial candidate Barnett. "If the Republicans win Pressler's seat, the Senate and the governorship, South Dakota is back where we started in 1968, with only McGovern in the Senate. So the stakes are tremendous."

Pressler, who won his last congressional election with a whopping 80 percent of the vote, is considered the early favorite in the race. He is challenged in the Republican primary by Ron Williamson, a former executive director of the State Municipal League, and a favorite of the party's conservative wing.

Barnett, who has mayor of Rapid City during the worst flood disaster in the state's history, was the only major Democratic candidate until mid March. At that time, Kenneth Stofferahn, a HUmboldt farmer who was elected a state representative as a Republican in 1974, entered the race, supposedly after being urged to do so by Abourezk and his staff.

Both Williamson and Barnett are running against Pressler's record as a "showboat congressman" more interested in press releases than in substantive legislation.

Running for the congressional seat being vacated by Pressler on the Republican side are Leo Thorsness, whom McGovern defeated in the Senate race in 1974, and state Treasure David Volk. Thorsness was a Vietnam prisoner of war: Volk was a bronze star winner there.

Tom Daschle, a former Senate aide to Abourezk, is running a low-budget door-to-door campaign on the Democratic side. Heis challenged by former congressman Frank Denholm, who entered the race late.