If you're on your way to divorce court in the District you may find yourself before a mediator instead of a judge.

In the latest effort to reduce its backlog of civil court cases, D.C. Superior Court started Monday offering free voluntary mediation to settle legal disputes involving divorce, child support, visitation rights, alimony, property distribution and other domestic relations issues.

The program can handle any domestic relations case filed with the court unless there was violence between the parties, the use of a weapon, evidence of child abuse or a "a severe lack of parity in bargaining power," said spokeswoman Linda Finkelstein.

"We're trying to get as many appropriate cases into mediation as possible," she said.

In the mediation session, instead of deciding the outcome of a case as a judge would, the mediator helps the two sides reach an agreement and no lawyers are necessary. No agreement is final until both parties consent to all the terms, and those dissatisfied with the mediation can still have a judge hear their case.

Superior Court Judge Gladys Kessler, who supports the mediation program, said the present court system almost requires people to become adversaries. "It is not a system geared toward conciliatory resolution of disputes. I think there is a great desire in the community for a less acrimonious and less bitter way to resolve domestic disputes," Kessler said.

Contested divorce cases that normally took up to a year to go to trial can be scheduled for a hearing before trained mediators, some of whom are lawyers with domestic relations training and experience, within four weeks, the program promises.

The new service is an expansion of the court's Multi-Door Dispute Resolution Program, an experiment that began in January with mediation of small claims disputes to save the court and citizens time and money.

That mediation program removed 1,000 cases from the court's docket since it began in April. Chief Judge H. Carl Moultrie I called that program "an extraordinary success."

The program is financed by the American Bar Association, which is spending $1 million to pay for 18-month dispute-resolution programs in the District, Houston and Tulsa.

Alternatives to litigation have gained momentum in recent years as judges all the way to the Supreme Court have complained that courts are becoming clogged with lawsuits.

In 1971, there were three mediation programs in the nation, compared to 300 today.

Mediation has moved into domestic relations because, while the number of new cases filed in the court's domestic relations branch has dropped 15 percent, the backlog of pending cases rose by 42 percent, according to the court's 1984 year-end report.

"Never before in this jurisdiction have separating and divorcing couples involved in contested cases had available to them any alternative in the court other than litigation," said Kessler, who formerly headed the court's family division.