The Justice Department is launching an experimental program to give the public a speedy and inexpensive way to resolve minor disputes through neighborhood justice centers that would serve as alternatives to the courts.

The centers would attempt, though mediation, to settle the sort of conflicts - domestic spats, claims by customers against merchants, arguments between landlords and tenants - that clog the dockets of the lower courts in American cities.

The centers and their services would be available to anyone willing to submit a dispute to mediation. But Justice Department officials believe they will be especially helpful to poor people who are denied access to justice because of the lack of money, education and time.

"We're trying to devise new means to alleviate the difficulty of many Americans in finding answers to small grieviences," explains Deputy Assistant Attorney General Paul Nejelski. "For many, litigation in the courts just isn't a practical answer. It's too costly and too time-consuming for the man of limited means who feels he's paid $25 for a pair of boots that aren't any good."

"At the same time," Nejelski adds, many of the traditional institutions that used to provide a framework for settling such disputes, such as the family and church, are losing their efficacy. Others like the justice of the peace, the policeman on the beat and the precinct captain are fading from the American scene."

As part of its search for substitutes, the Justice Department hopes to have three neighborhood centers, funded with federal money but under local control, in operation by the fall.

Although the lans are still tentative, department officials say it seems fairly certain that one will be in Los Angeles and one in Atlanta. The third is expected to be in the Midwest.

The experimental centers will be evaluated closely over a 15-to-18-month period, and department officials are hopeful that the experiment will spur cities all over the country to set up their own neighborhood centers.

To assist such efforts, the department has plans for a "national resources center" that would serve as a clearinghouse for information and technical assistance for local governments wanting to try the idea.

The impetus for this program comes from Attorney General Griffin B. Bell, who has established as one of his main priorities a drive to provide better access to justice without putting an unbearable strain on the resources of the federal, state and local courts.

To direct this compaign, Bell has set up an Office for Improvements in the Administration of Justice under Assistant Attorney General Daniel J. Meador, a former law professor at the University of Virginia. Meador's office already is involved in seveal initiatives to speed for arbitration of certain cases in the federal courts and recently introduced legislation to broaden the jurisdiction of federal magistrates.

Of all the plans, though, Bell is known to regard the neighborhood justice centers as potentially the most important. He has said that he wants the program to demonstrate how the federal government can play "a leadership role" in assisting the states and cities to improve the quality of justice.

To this end, he directed that the experiment he financed by federal funds through the Law Enforcement Assistance Administration. Department officials estimate the costs at $150,000 each for the three prototype centers and an additional $300,000 to $350,000 for evaluation of their operations.

The planning has been done primarily by Nejelski, one of Meador's deputies, and by John Beal, a department attorney. Both say that a great deal of trial and error will be necessary to learn how the centers can operate most efficiently.

Each center will have an administrator, who may or may not be a lawyer, some paralegal assistants and a cadre of mediators, recruited, if possible, from the neighborhood served by the center and given special training.

"We hope to recruit from retired persons, housewives and others who know the people of the neighborhood and their problems," Nejelski says. "If, for example, you have a dispute involving a family who are Black Muslims, it would be important to have a mediator who is also a Muslim or at least familiar with their traditions and sensibilities."

Establishment and control over the centers will be accomplished in a variety of ways. In Los Angeles, the department is working through the local bar association, while the projected Atlanta center probably will be tied to the local courts. Each center also will have a citizens' advisory board representing the ethnic, economic and social composition of its neighborhood.

They will be geared to handle cases referred by public and private agencies and what Nejelski calls "walk-ins from the street." A primary task of each administrator, he adds, will be to ensure that the people of the neighborhood are aware of the center's services and be encouraged to put their trust in it.

Nejelski notes that the centers are certain to encounter some cases that they cannot handle, either because one of the disputants will not agree to mediation or because they involve issues that require the intervention of a lawyer. In such instances, he says, the centers will assist the parties to a dispute in going to court or seeking some other legal remedy.

Both Nejelski and Beal point out that these general guidelines still leave a lot of unanswered questions. They range from whether chain stores and municipal agencies, which might be parties to a dispute, will cooperate in submitting to mediation to the type and premises and working hours that would be most appropriate for the centers.

"That might sound trivial," Mejelski says, "but there are real problems in whether people might find a store-front location less intimidating than a public building. If you schedule mediation sessions at night when people aren't tied up at work, will they be afraid to come because of a high crime incidence in the streets?

"These are all things where we're still groping for answers, and that's why we're starting in a small way with only three centers. We hope their experience will tell us what's good and what's bad and which way we should go in the future."