Dismay, disarray -- and delight -- are sweeping Illinois' political camps after primary victories by two far-right candidates at the top of a statewide Democratic slate headed by Adlai E. Stevenson III.

Although the former U.S. senator remains optimistic, Stevenson's campaign to beat Republican Gov. James R. Thompson in the Nov. 4 election is in deep trouble. The campaign has been strapped for cash -- Stevenson recently loaned it $35,000 to help keep operations afloat -- and Tuesday's results have left it stalled.

Ahead is an exhausting effort of uncertain outcome to escape the unwanted embrace of lieutenant governor candidate Mark Fairchild and secretary of state nominee Janice Hart, who are backed by Lyndon H. LaRouche Jr., the Leesburg, Va., activist.

LaRouche and various groups tied to him urge repeal of the Gramm-Rudman-Hollings budget control act, call for a strong national defense that includes the president's Strategic Defense Initiative, and advocate screening of all Americans to detect AIDS and quarantining those with acquired immune deficiency syndrome until a cure is found.

Stevenson, who vowed this week he would not be on a ballot with Fairchild and Hart, condemned them as "neo-Nazis who preach hatred and bigotry."

Stevenson's legal team is examining the Fairchild and Hart campaigns for technical violations of state election requirements, such as filing and residency errors. Stevenson's people also are searching for any arrest records or felony convictions, which could disqualify them.

Aside from a misdemeanor charge against Hart for allegedly disrupting a local synagogue service last year, no legal troubles have been reported about the LaRouche candidates. A misdemeanor does not disqualify a candidate for statewide office in Illinois.

If the legal search fails, Stevenson faces what he has termed "the least desirable alternative" of all: setting up a third party.

So far, few senior party officials or candidates have expressed an inclination to join him in forming a third party. Sen. Alan J. Dixon, the party's most senior Illinois officeholder, has counseled Stevenson to run with Fairchild, disavow him and pledge to eliminate the largely ceremonial office if elected.

But relations between Stevenson and Dixon have been cool ever since Stevenson, ignoring tradition, refused to quit his Senate seat a few days before his term expired in 1980 so Dixon could be appointed and gain seniority on other freshmen elected that November.

Sen. Paul Simon, widely regarded as the voice of the party's liberal wing, has warned he will not vote for his close friend Stevenson if Fairchild is on the same ticket.

Stevenson, who has expressed abhorrence that Fairchild could stand "a heartbeat away from the governorship," kept an upbeat, determined demeanor. "This has brought us worldwide attention," he said after taping for a weekend television program. "Calls are flooding in. Donations will pick up."

The disagreement over how to proceed could blossom into a bitter feud tinged with moral arguments. Stevenson says he cannot believe Democrats will run with Fairchild and Hart if he is forced to organize a new party. While numerous party officials blame him for a lackadaisical primary campaign, Stevenson says he "did everything I could" to assure victory of his handpicked "dream ticket" slate.

Meanwhile, Thompson's reelection chances, which recent polls indicated were not rosy, have soared. "We were going to conduct a poll right after the primary to see how things looked," said one of his advisers, "but maybe we won't need it -- ever again."

The governor, who narrowly beat Stevenson in 1982, has been careful to say little except to chide the Democrats for "taking the voters for granted." But the outline for his response to the presence of Fairchild and Hart among Democratic regulars is taking shape. He has said he is appalled.

"I never thought Jim Thompson could become the darling of the liberals," said one Democratic activist. "But Adlai may have accomplished the impossible."