A growing number of integrated suburbs in the United States, fearful that resegregation will occur, are financing existing fair-housing efforts and starting new governmental programs to maintain racial balance in their communities.

Suburbs around Cleveland, Chicago, Detroit, St. Louis, Northern New Jersey, Long Island, N.Y., Hartford, Conn., and other metropolitan areas have become magnets for black home seekers while nearby towns remain virtually all-white. The suburbs' officials have filed suits against real estate brokers, charging racial discrimination and steering.

They also are marketing their towns to continue to attract a variety of residents and have supported fair-housing groups that work to expand housing opportunities for home seekers.

Few such housing-discrimination suits have been initiated in the Washington area. However, late last year, a federal judge in Alexandria ruled that an apartment complex discriminated against an interracial couple in Northern Virginia and ordered payment of an expected $30,000 in damages, court fees and attorneys' fees. Meanwhile, in a separate housing-discrimination case brought by the Arlington County government, an apartment complex agreed to train its employes in fair-housing law and take other measures to ensure compliance with fair-housing statutes.

A year ago, Ohio's Housing Finance Agency set aside 10 percent of a $347 million tax-exempt mortgage revenue bond issue for black first-time home buyers moving into areas that were less than 10 percent black and white first-time buyers moving into areas less than 60 percent white.

"Before, there were only a couple communities looking at this issue," said James Engstrom, a staff associate with the Fair Housing Legal Action Committee in Park Forest, Ill., which is supported entirely with funds from 12 Chicago suburbs and federal money under the Community Development Block Grant program that is allocated by Cook County. "As more communities become integrated, more begin looking at it from a governmental standpoint."

Despite extensive municipal activity, governmental support for integration maintenance and other affirmative marketing efforts still has at its roots community action, according to Charles Bromley, executive director of National Neighbors, a coalition of local fair-housing organizations that is based in Washington.

"There's never been an example where a city jumped up and said we ought to do this," Bromley said. "Every municipal effort to create balanced, integrated-living patterns is directly related to the presence of a successful community organization which has put pressure on the local government."

But, as more communities open to minorities while others remain closed, more municipalities will be forced to act, he and others said.

The Park Forest fair-housing legal group, which was started by seven suburbs in November 1981, has initiated eight suits against real estate brokers and landlords, Engstrom said. Four of these have been settled and four are pending, he said. In the settlements, black plaintiffs won damages ranging from $7,000 to $12,000, as well as agreements from brokers and landlords to establish affirmative-marketing plans and fair-housing training for their employes.

"An island of equal opportunity is in grave peril in a sea of inequality," said Donald deMarco, director of the Department of Community Services in Shaker Heights, Ohio, which promotes housing integration in his and other Cleveland suburbs.

DeMarco said that his city department works with cooperative real estate brokers and even offers financial incentives, including interest-rate buy-downs, monthly mortgage supplements and down-payment loans to home buyers who move into areas where their race is "underrepresented." The city also successfully has filed suits against brokers who have engaged in racial discrimination or steering.

Judy Airhart, executive director of the Cuyahoga Plan in suburban Cleveland, which receives some federal Community Development Block Grant money, said that the increasing municipal support for integration maintenance and affirmative-marketing programs is a "positive move because it's important to get some of these programs institutionalized."

Her group promotes integrated housing through the use of brochures and counseling and has been a plaintiff in numerous housing-discrimination and racial-steering cases.

Also in the Cleveland area, Cleveland Heights and University Heights, as well as Shaker Heights, have their own government programs, and all three have joined with two school districts to create the East Suburban Council for Open Communities.

The council, which obtains half its $250,000 annual budget from the five governmental bodies, uses advertising and brochures to promote housing integration, including increasing options for black home seekers, and provides escorts and other housing services to home seekers.

"In a year's time, more than 100 black families have moved into the six communities with less than 2 percent black population which we targeted," Executive Director Winston Richie said.

The University City (Mo.) Residential Service was started by community leaders "to stop the block-busting and the peddling of fear" in the St. Louis suburb when blacks began moving there in 1968, Executive Director Lorine Compton said. The town's government began providing funding and free office space a decade ago.

"We're here to encourage people to look for housing in U-City," said Compton. "There still is steering, and you have to keep on top of it. When we find that steering has occurred, we turn the information over to the city attorney who writes a letter to the Metropolitan Real Estate Board."

In the greater New York city area, the Teaneck, N.J., government supports a Housing Information Services program, which markets itself and its neighbors to a broad spectrum of potential residents. The cities of Freeport on Long Island in New York and Bloomfield, Conn., have undertaken their own marketing programs.

In the Chicago suburban area, in addition to the fair-housing legal group's efforts that are oriented toward the south suburban area, several fair-housing offices in the western suburbs are supported by Oak Park, Bellwood and other municipalities, which have seen their black populations swell while neighboring suburbs have remained virtually all-white.