After E.I. duPont de Nemours & Co. completed its $7.3 billion acquisiton of Conoco Inc. last week, some troublesome indigestion seemed inevitable.

How would Du pont repay the $4 billion in new borrowing it took on to win the bidding war for Conoco, which tripled its traditionally conservative debt burden, and would this debt checkmate Du Pont's other plans for expansion in high-technology area?

Would Seagram's Edgar and Charles Bronfman use thie new 20 percent holdings of Du Pont's stock to make a move against Du Pont's management, perhaps compelling Du Pont to buy them out with the sale of valuable coal or oil properties?

And how would the pieces of the largest corporate merger be assembled into a coherent new company that could take advantage of its new power without stumbling from its own size and weight? Given the depressed earnings in oil products and chemical - two of Conco's greatest strengths - would the merger be a drag on the earnings of the new Du Pont?

Outsiders believe it will be many months before it becomes clear whether the $15-billion Du Pont is having trouble absorbing the $20-billion Conoco. "Just the merging of their tax and accounting practices will take a while," said Richard Derbes, an analyst with Oppenheimer & Co. in New York.

The initial stages of the merger may be calmer than had been expected, however.

Edward G. Jefferson, Du Pont's chairman, says the speculation about a showdown between Seagram's and the Du Pont family, which owns about 30 percent of Du Pont's stock, is "unfounded." In an interview following the conclusion of merger arrangements Thursday, Jefferson said he has met several times with the Bronfmans, chairman Edgar and deputy chairman Charles. Although he said the discussions are still in midstream, "I can assure you they have been constructive."

The Seagram camp also put out word last week that no raiding party was being formed to assault Wilmington and no demands will be made for an exchange of oil or coal reserves for Seagram's will settle back into the quiet, happy life of a 20 percent shareholder in Du Pont with several seats on the Du Pont board. "Essentially, the story's over," predicted on close observer.

The way Seagram figures it, it sold its Texas Pacific Oil and Gas Co. subsidiary for $2.3 billion in August 1980 and used that money to buy its stake in Conoco. Seagram's Conoco stock became Du Pont stock with the merger; thus, in a sense, Seagram swapped Texas Pacific and its 1980 after-tax u.s. earnings of $68 million for a 20 percent interest in the combined Du Pont and Conoco, worth nearly $350 million using last year's earnings for the two companies. A good deal, in Seagram's eyes.

Whether Du Pont dividen checks will really keep Seagram happy remains to be seen. A number of Wall Street analysts expect that the new company's earnings growthin the immediate future will inevitably be slower than Du Pont's record before the merger. Conoco is a possible anchor on Du Pont, some analysts say, because it has not kept up with energy industry leaders in oil and gas exploration and refinery modernization.

What Conoco has, however, is wealth in the ground and under the sea-14 billion tons of coal, along with its oil and gas reserves. Du Pont is preparing to sell some of these reserves even without direct pressure from Seagram for higher profits.

Jefferson says he is committed to repaying a large part of the $4 billion Du Pont borrowed to get Conoco and restore the "financial flexibility" that Du Pont used in winning the merger battle. Du Pont's debt-to-equity ratio now is an uncomfortable 60 percent, compared with the traditional 20 percent level, and the annual interest charges it now faces on the acquisition debt is almost as much as its 1980 earnings.

Some natural resource assets that aren't needed for the operations of Du Pont or Conoco in the coming decade can and will be sold over the next three years, he said, He didn't disclose where.

I'm not going to get myself trapped selling too low," said Jefferson. "On the other hand, I'm determined to really dent this acquisition debt."

Where Du Pont says it is not in a hurry is in the complex merger of the chemical and manufacturin processes of the two giant firms.

On paper, the marriage makes perfect logic: 70 percent of Du Pont's sales come from products made from crude oil and natural gas feedstocks, and Conoco, the nation's ninth-largest oil company, could meet Du Pont's needs.

Du Pont has been trying to lock up secure supplies of oil and gas feedstocks since the disastrous aftermath of the 1973 Arab oil embargo, when soaring costs of oil-based raw material and depressed prices for fibers and plastics caught Du Pont in an excruciating squeeze. Its earnings fell from $12.04 a share in 1973 to $5.43 two years later, and the fact that Du Pont was dependent then on feedstocks from one of its key rivals, Dow Chemical Co., was a lesson that Du Pont remembered.

Du Pont was seeking its own feedstock supplies when it began a joint venture with Conoco in 1978 to find natural gas in Texas, Louisiana, Mississippi and Alabama, and that relationship led directly to the alliance between the two companies this summer to fight off the take-over bids by Seagram and Mobil Corp.

However, the merger of Conoco's oil and gas production to Du Pont's manufacturing needs will not be immediate, the two companies say, because much of the production is already under contract.

"in the short run, there's nothing that Conoco's going to do for Du Pont" in shifting Conoco's production to Du Pont, said Harold May, Du Pont vice president for materials and logistics. "We will abide by our long-term contract," says Constantine Nicandros, Conoco's executive vice president for petroleum products. "There's no great rush for us to tear up our businesses to do something different today," he said. But to the extent that the pieces fit, the two companies will take advantage of it, he added.

One immediate example is Du Pont's recently announced joint venture with PPG Industries Inc. to produce ethylene glycol, used in synthetic fibers preparation. Du Pont expects to supply at least its share of the ethylene feedstocks from the Conoco refinery at Chocolate Bayou, Texas, and perhaps more, Du Pont says.

And as Conoco's existing contracts expire in the next three to five years, Du Pont will have first claim on the production for its own uses, Jefferson said. By the second half of the 1980s, Du Pont should be able to get its entire hydrocarbon feedstock needs from Conoco, either directly or through swaps, he said.

The most practical fit between the two companies in the near future will be economic. When oil and gas prices shoot upward, the profits of chemical and synthetic fiber manufacturers generally suffer. When energy companies' prices and profits are flat, that usually spells good times for manufacturers that depend heavily on oil and gas feedstocks. The Conoco-Du Pont merger should help cushion the cyclical slumps both companies have faced, their officials say.

"To a considerable extent, the synergism is financial. Together, you create a much more solid financial entity," said Nicandros.

The other fit that Du Pont and Conoco will have to master is the blend of their executives. Du Pont's pledge to retain Conoco's management was a key factor in their agreement to join forces against Mobil and Seagram, and the new organization chart announced by Jefferson last month makes good the promise. Ralph E. Bailey, chairman of Conoco before the merger, now is one of two vice chairmen of the new Du Pont, under Jefferson. The other is Richard E. Heckert, Du Pont's vice chairman.

Bailey also is chief operating officer of Conoco, with Jefferson, former Du Pont chairman Irving S. Shapiro and Du Pont's oil expert David K. Barnes as nonvoting members of the Conoco subsidiary executive committee.

Jefferson, at one time Du Pont's research chief, insists the merger won't divert Du Pont from the future it sees in new high-tecnology ventures-from sophisticated medical diagnostic equipment to the products of gene splicing and other life-science breakthroughs.

The final word on Seagram's involvement with Du Pont as the other, unintended "partner" in the merger may well depend on whether it shares Jefferson's excitment about this future.