Two of the world's largest offshore oil construction companies yesterday pleaded no contest to federal indictments charging a conspiracy to rig bids in violation of anntitrust law. Both firms were immediately fined $1 million each.

A federal grand jury in New Orleans handed up indictments against Brown & Root Inc. of Houston and J. Ray McDermott & Co., Inc. of New Orleans. The indictments charged the companies with conspiring to rig bids for marine construction projects in violation of the Sherman Antitrust Act.

In addition to the companies, the grand jury charged six executives of the two firms with bid-rigging as well as mail and wire fraud. The executives did not enter a plea yesterday.

U.S. District Court Judge Lansing Mitchell gave the two firms 10 days to pay the fines. The fines were the maximum allowable under the law.

A spokesman for McDermott said the company was not admitting guilt, but had decided on its plea in an effortto avoid a time-consuming trial. A Brown & Root spokesman in Houston declined to comment, except to confirm the pleas and fines. Therewas no immediate response from the company executives.

The companies were accused of attempting to maintain artificially high prices and eliminate any competition in the extremely profitable business of building offshore pipelines and oil production platforms.

Executives named in the grand jury indictments were:

Charles Leonidas Graves, chairman of the board and chief executive officer of McDermott, who was charged with nine mail fraud counts and one wire fraud count.

Robert Kenneth Richie, president of McDermott, charged with one count of mail fraud.

Hosea Ware Bailey, executive vice president of McDermott, charged with eight counts of mail fraud and one count of wire fraud.

Henry Rogers Reeves, group vice president of McDermott, eight mail fraud counts and one of wire fraud.

Hugh Wescott Gordon, Jr., executive vice president of Brown & Root, charged with nine counts of mail fraud and one count of wire fraud.

Edward Lacy Tallichet, senior group vice president of Brown & oot, nine counts of mail fraud and one count of wire fraud.

According to Ky P. Ewing, acting assistant attorney general in charge of the Antitrust Divisn, the defendants are charged with conspiring to allocate among themselves certain contracts for marine construction services, and to submit rigged bids during a period from at least 1960 through 1975.

The defendants allegedly exchanged bid price information and submitted collusive bids to several customers in the oil and gas industry seeking to build subsea pipelines and offshore platforms in the Gulf of Mexico and elsewhere.

The maximum penalty upon conviction under the Sherman act for each individual is three years in jail and a $100,000 fine.

The mail and wire fraud violations, if resulting in conviction, would subject the six individuals to five more years in jail and a $1,000 fine for each count.

McDermott showed sales of $1.7 billion and profits of $146 million during its last fiscal year. Brown & Root, a subsidiary of the Halliburton Co., does not report its earnings separately.