Followers of political extremist Lyndon H. LaRouche Jr., who stunned Illinois Democrats by winning the party's nominations for lieutenant governor and secretary of state nearly two months ago, have failed to follow up with any significant victories in the first primaries since then.

About 35 LaRouche candidates ran in U.S. Senate and House primary races in Ohio, Indiana and North Carolina on Tuesday, and in the Texas primary last Saturday. Three LaRouche supporters, running unopposed, won Democratic congressional nominations: two in Texas and one in Ohio.

LaRouche candidates ran in the Democratic Senate primaries in Ohio, Indiana and North Carolina, and in 14 House races in Ohio, eight in Indiana and 11 in Texas. In addition, about 20 LaRouche supporters ran for Democratic county chairman posts in Texas.

A LaRouche supporter, Clem Cratty, was the only Democratic candidate in the primary for Ohio's 4th Congressional District, but party officials said they were preparing to back a candidate who will file as an independent and run as the "real" Democrat against Rep. Michael G. Oxley (R-Ohio).

In Texas, unopposed LaRouche backers won nomination in the Democratic primaries in two strongly Republican House districts in Houston where Democrats historically have not fielded candidates. LaRouche supporter Susan Director will oppose Rep. Tom DeLay (R-Tex.) and Harry Knissen will challenge Rep. Bill Archer (R-Tex.).

In addition, a LaRouche supporter is in a runoff for the Democratic chairmanship of Bexar County (San Antonio).

A former LaRouche backer, Don Jones, was the only candidate to file for the Democratic primary in Ohio's 6th Congressional District, but state party officials said Jones had renounced his support for LaRouche and had convinced local party leaders that he would run as a "regular" Democrat against Rep. Bob McEwen (R-Ohio). Both the 4th and 6th districts are heavily Republican: Oxley and McEwen each won about 75 percent of the vote in 1984.

Another LaRouche backer in Ohio, Don Scott, won 15 percent of the Democratic primary vote against Sen. John Glenn.

In Indiana, Jill L. Long, a university professor and Valparaiso city councilwoman, won the Democratic Senate nomination with 74 percent of the vote over LaRouche supporter Georgia Irey, and a LaRouche supporter finished ninth in a field of 10 in the North Carolina Senate primary, won by former governor Terry Sanford.

In Illinois, Mark Fairchild, the LaRouche supporter who won the Democratic nomination for lieutenant governor, declared that he is now the party's gubernatorial candidate because Adlai E. Stevenson III, who topped the Democratic ticket in the primary, resigned rather than run with Fairchild and Janice Hart, a LaRouche supporter who got the nomination for secretary of state. Stevenson is attempting to run for governor as an independent.

"A lieutenant governor assumes the role of the governor should the office of governor be vacant, by right of succession," Fairchild said. "In like manner, I must therefore assume the role of the Democratic nominee for governor."

A member of the Illinois Board of Elections, however, said there was no legal process by which Fairchild could do so.

"There's no statutory process for him to move up to the governor's slot," the official said. "There doesn't seem to be any way for that procedure to be possible."

Stevenson is asking Illinoisans to vote the Democratic ticket, except for Fairchild and Hart, and has filed a lawsuit seeking to clear the way for him to run as an independent in his effort to unseat Republican Gov. James R. Thompson. If Stevenson fails, he has said he will form a third party with a full slate of candidates for statewide offices.