CHICAGO (AP) _ Two Lyndon LaRouche supporters who won Democratic primary races are entitled only to appear on the general election ballot, and are not automatically entitled to party support, a judge ruled today.

Mark Fairchild and Janice Hart had sought a preliminary injunction against activities on the part of the chairman of the Democratic Central Committee of Illinois that they said were hampering their campaign.

The motion said chairman Vince Demuzio had excluded the two from normal Democratic aid to statewide candidates, including access to mailing lists; had denied them access to two party headquarters; had tried to remove them from the ballot; and had supported Adlai Stevenson's third-party bid for governor.

Cook County Circuit Judge David Shields denied the injunction request.

''All the candidates are entitled to is to be on the ballot,'' said Shields.

Fairchild won the Democratic nomination as lieutenant governor while Hart won the secretary of state's race in the March 18 primary. Their victories prompted Stevenson to resign as the Democratic gubernatorial candidate and form a third party.

Attorneys for Demuzio argued that the U.S. Constitution allowed the party and the individuals who comprise it to decide for themselves whom they will support. They also said Democratic rules do not specify that all Democratic candidates should receive aid.

''One person cannot force another to believe and support somebody,'' said defense attorney James Stamos.

The two backers of LaRouche, a political etremist, planned to appeal today's ruling, Fairchild said.