The multibillion-dollar bidding derby for Hughes Aircraft Co. is moving toward the wire, and one of the participants says the competition for the huge aerospace company founded by Howard Hughes is "most severe."

"There are some big, big boys playing in that particular playpen," said Forrest N. Shumway, chairman of Signal Cos., speaking at his company's annual meeting last month.

The other rumored bidders against Signal for Hughes are General Motors Corp., Allied Corp., Ford Motor Corp., General Electric Co. and Boeing Co., and at least one bid may involve a joint effort by two companies.

The bids were due the middle of this month to investment banker Morgan Stanley & Co., which is handling the auction for the company's present owner, the Howard Hughes Medical Institute.

Sources have said that the institute expects to receive five bids for the company, which is based in El Segundo, Calif. A possible buyout by the company's 68,000 employes fell by the wayside as bidding increased.

Analysts have estimated that Hughes Aircraft could fetch between $4 billion and $6 billion, which would make it one of the heftiest corporate acquisitions ever. Whoever gets it will gain control of one of the nation's top defense contractors. In spite of its name, it never has manufactured a single airplane, concentrating instead on sophisticated electronics, missiles and communications satellites.

Last year, the company had $4.9 billion in sales -- it does not report income -- $6 billion in new orders and a $12 billion year-end backlog. Its remarkably low $78 million in long-term debt makes it additionally attractive, because it would allow an acquirer to borrow heavily against the company's assets to pay for the acquisition.

Hughes will provide the winning bidder with a steady cash flow and income stream from the relatively stable defense contracts it holds.

For Signal and Allied, Hughes would represent a chance to diversify into areas that complement their existing high-tech businesses. General Electric has been known to have had a $5 billion acquisition war chest for some time. Ford and Boeing could use the company to bolster their already burgeoning aerospace businesses. And General Motors has been known for years to be interested in moving strongly into defense work; in addition, its chairman, Roger Smith, for months has been mysteriously promising a "lulu" of an announcement.

Irving S. Shapiro, the former chairman of E. I. du Pont de Nemours & Co. Inc. and a member of the Hughes Medical Institute board, said the winning bid is likely to be announced shortly after all the offers are in.

"If you've got cash bids, the answer could be the same day, almost," Shapiro said. However, he said he expects the offers to be somewhat more complicated, which would lengthen the analysis and delay an announcement for days or weeks.

"We've got to be sure we can understand each bid and be able to evaluate it," Shapiro said.

Howard Hughes set up the medical institute in 1953 to shelter the company's profits from taxes. Income from the company funds the institute's research into endocrinology, immunology and genetics.

After Hughes' death in 1976, Hughes Aircraft became embroiled in a variety of legal disputes over its ownership. The key challenge came from Delaware officials, who charged that the institute was not receiving enough income from the company. In 1983, for instance, it reportedly made a $51 million profit for the institute on revenue of $4.9 billion. And that was one of the better years.

Last year, a Delaware judge settled many of the questions by ordering the appointment of a new board of trustees for the institute, including Shapiro and several other prominent businessmen. The new board re-evaluated the institute's holdings in Hughes Aircraft, and early this year announced plans to sell the company and invest the proceeds elsewhere. The board felt that the institute could vastly increase its income with a $4 billion to $6 billion windfall from selling Hughes. Indeed, the medical institute is becoming quite anxious to complete the sale of Hughes Aircraft, Shapiro said. "Every day that we wait to get our money is costing us a huge amount of interest," he said.