WASHINGTON (AP) _ The Supreme Court today agreed to take a new look at the right of alleged child abusers to question their young accusers in court.

The court said it will hear an appeal by an Illinois man sentenced to 10 years in prison for sexually abusing a 4-year-old girl.

The justices said they will decide whether young children who are available to testify must take the witness stand in such cases when other witnesses have testified that the child told them she was abused.

In another matter, the court, complaining about being burdened with ''frivolous'' appeals, voted 6-3 to crack down on some of the people who file them.

In an unsigned order, the court changed one of its procedural rules so that it can strip some poor people of the privilege of filing appeals without having to pay a $300 filing fee and significant printing costs.

The three dissenters called the action a ''serious mistake'' that creates an ''invidious distinction'' between the rich and the poor.

In the child-abuse matter, the justices last year said the constitutional right of defendants to confront their accusers is not absolute. The court allowed states to shield young witnesses from face-to-face confrontations with child-abuse defendants - permitting use of videotaped testimony, closed- circuit television and testimony by those who interviewed the alleged abuse victims.

But the court said judges must have evidence the child faces the risk of serious emotional trauma before barring a face-to-face confrontation.

The issue of availability of a child witness was not addressed by the high court in the case decided last year.

The justices said today they will hear an appeal by Randall D. White and probably will rule sometime in 1992.

White was convicted of entering a Georgetown, Ill., home in the early morning hours of April 16, 1988, and molesting a girl identified as S.G.

The child did not testify at his trial. But five witnesses - the child's babysitter, her mother, a police officer, nurse and doctor - said S.G. told them she was assaulted.

An Illinois appeals court ruled that S.G.'s statements to the babysitter, mother and officer were spontaneous declarations made soon after the attack. The appeals court said the statements the child made to the doctor and nurse some time later also are admissible.

''Illinois courts have recognized that special circumstances exist concerning the motivations behind the statements of very young children,'' the state court said. ''The reason that their statements are admitted is that it is unlikely that a child of tender years will have any reason to fabricate stories of sexual abuse.''

The state court also said that a state law against child abuse also authorizes hearsay evidence by medical personnel.

''Whether the (alleged victim) is unavailable is totally irrelevant to the determination of whether an out-of-court statement of that declarant is admissible under an exception to the hearsay rule,'' the state court said.

Lawyers for White said, ''Since there was no showing of unavailability in this case, fairness dictates that the defendant should have been given an opportunity to cross-examine his accuser.''

In other action today, the court:

- Agreed to decide whether employers may impose wage cuts or other changes in working conditions before bargaining talks with unions formally reach an impasse.

The court said it will hear Bush administration arguments that a Louisiana company violated federal law when it reduced salaries before negotiations with union representatives reached a stalemate.

- Agreed to decide whether states and counties may tax Indian-owned land on reservations.

The court, setting the stage for a ruling that could have broad impact for tribes and their members, said it will study a dispute over taxes imposed on land within a Yakima Indian reservation in Washington state.

- Allowed Mississippi juries to be told whether convicted murderers ever would be eligible for parole if sentenced to life in prison rather than death.

The justices, without comment, let stand the Mississippi Supreme Court's throwing out of Kevin Turner's death sentence because his jury was not told, as he requested, he never would be released if given life in prison.

The child-abuse case is Randall White vs. Illinois, 90-6113.