San Juan Racing Associates Inc., owner of local radio stations WJMD-FM and WUST-AM, eight other stations and a race track, is asking shareholders to approve a plan to sell all the company's assets and go out of business.

As part of the plan, the two Washington radio stations will be sold to a Texas company, which will then resell WUST to District Group Communications Inc., a local company headed by James McQueen.

The liquidation proposal will be put to a vote at San Juan Racing's annual meeting next Tuesday at the company's El Commandante Race Track in Puerto Rico.

San Juan Racing has been trying for more than three years to gear down its operations because most of its officers and directors are getting too old to run the company.

Two long-time San Juan board members, law partners Joseph Danzansky and Raymond Dickey, have died since the search for a buyer began. Other directors include Robert A. Philipson, 82, head of a Washington accounting firm, and local attorney Marvin Willig, 67.

Gulf Broadcasting Corp. of Dallas has agreed to buy seven of the eight radio stations for a total of $65.75 million as the first step toward liquidating the operation, San Juan disclosed in its annual meeting notice.

Gulf Broadcasting is a subsidiary of Gulf United Corp., an insurance and broadcasting company, which two years ago acquired Equitable General Insurance Co. of McLean.

In return for all the stock of SJR Communications, a broadcasting subsidiary, Gulf Broadcasting will pay San Juan $60.5 million cash and assume $5.25 million in debts.

Because the purchase will give Gulf more stations than any one company is permitted to own under federal regulations, four of the stations will be resold, an attorney for the firm said.

The Federal Communications Commission already has approved transferring WUST to McQueen's company, which reportedly plans to keep the station's programming oriented toward black audiences. No changes in the opertion of WJMD have been discussed, a Gulf spokesman added.

San Juan officials estimated that liquidation of the company's assets will yield stockholders more cash than the market value of their stock, which has sold recently for about $20 a share.

Cash from the sale of SJR Communications will be distributed directly to stockholders shortly after the transaction is completed later this year. Shareholders are expected to get about $13.50 per share from that sale.