Trustees of the Hughes Medical Institute met for several hours yesterday but failed to decide on a buyer for the institute's principal asset, defense-contracting giant Hughes Aircraft Co.

The nine trustees were considering bids for the company from General Motors Corp., Ford Motor Co. and Boeing Co. The winner is expected to have to pay between $4 billion and $6 billion for the El Segundo, Calif., company, which had $4.9 billion in revenue last year, two-thirds of it from defense contracts.

The legacy of billionaire Howard Hughes, Hughes Aircraft is a leading maker of missiles, communications satellites and sophisticated electronics equipment. Hughes set up the medical institute as owner of the company in the 1950s primarily to shelter the company's income from taxes.

The institute is selling the company because the trustees believe the institute can get a better return on its assets if they are invested elsewhere. In 1983, the last year for which figures are available, the company produced $51 million in profits for the institute's use; last year, the income directed to the institute was reportedly about $80 million. The institute conducts research in the fields of genetics, immunology and endocrinology.

The sale also is expected to remove pressure on the institute from the Internal Revenue Service and from officials in Delaware -- the state in which the company and institute are incorporated -- who have complained that the arrangement appears to be more tax shelter than a good-faith effort to raise money for the institute.

The board of trustees, which includes business executives such as former E. I. du Pont de Nemours & Co. Inc. chairman Irving S. Shapiro, was set up last year by a Delaware judge to address this criticism and to settle a longstanding battle for control of the institute. Like many of Howard Hughes' other affairs, control of the institute -- and hence the company -- was clouded after the billionaire's death in 1976 by the absence of a valid Hughes will. Delaware officials and a relative of Hughes had charged that some of the billionaire's associates took advantage of the confusion following his death to improperly take control of the institute.

The trustees' call earlier this year for bids for the company attracted interest from some of the nation's biggest industrial firms, but the final bids are believed to have come from Ford, GM and Boeing. Tight security on the bidding process has made gathering details of the status of the bids virtually impossible, but Morgan Stanley & Co. is known to have screened the bids on behalf of the institute and is believed to have made a recommendation to the trustees.

Analysts have said that whatever company winds up with Hughes Aircraft, it will be adding to its holdings a solid performer with a steady income stream and extremely strong technological expertise.