THEY CALL themselves "International Six Incorporated," and in the past couple of years that global half-dozen has included:

Dr. Omar Zawawi, the Harvard-educated brother of the foreign minister of Oman, that tiny Persian Gulf nation suddenly so vital to U.S. military strategy in the Middle East.

Maj. Gen. Brent Scowcroft, who succeeded Henry Kissinger as the top White House adviser on national security during the Ford administration.

Col. John V. (Jack) Brennan, the trusted White House aide who resigned from the Marine Corps to follow President Nixon into exile at San Clemente.

Warren L. (Bill) Gulley, head of the White House Military Affairs Office under three preidents; a man to be feared and courted when he held that job and a man with a vast network of friends and contacts, civilian and military, here and abroad.

Marvin Watson, the Lyndon B. Johnson aide who was postmaster general in 1968 and later become head of Occidental Petroleum's international operations. In 1976 he pleaded guilty to a misdemeanor charge growing out of an illegal $54,000 contribution by the head of Occidental to President Nixon's 1972 reelection campaign.

Haywood R. Smith, another LBJ military aide who later distinguished himself as a helicopter pilot in Vietman.

Just the fact that top White House aides from the past three administrations ended up in business together would be enough to focus attention on "ISI," a Panamanian-registered corporation that now has offices at 1875 I St. NW.

Officially, the "International Six" are "business and investment consultants." But the nature of their business, investing or consulting is not something they choose to discuss.

The involvement of Zawawi, a financial adviser and unofficial roving ambassador for the pro-Western sultan of Oman, intensifies interest, particularly at a time when Oman has become a critical supply link to the U.S. naval fleet operating in the Indian Ocean and the Omani government is building up defenses with a shopping list for weapons that could run into the billions.

Zawawi, who owns at least two apartments here in Foxhall East on Massachusetts Avenue, is currently believed to be back in Oman.

When Shirley Temple Black was U.S. chief of protocol in Washington in 1976 and 1977, she and her husband, former Naval Intelligence Officer Charles A. Black, lived in one of those apartments.

At that time, Charles Black was being accused in the press here and abroad of fronting for the CIA and the U.S. Navy in a project involving the "surveying and developing" of a fishing industry in Oman.

Black, still a consultant to Oman who recently completed a project involving maritime traffic in the strategic Strait of Hormuz, said last week that Zawawi had also been his landlord in Oman. Black's offices in Oman were located in a building constructed and leased by Zawawi.

Zawawi, a medical doctor, was minister of health in the Eastern Province of Saudi Arabia until the 1970 coup that brought the current ruler into power.

Most of Zawawi's fortune has been acquired in one decade. One of his companies, Waleed, represents Swedish hospistals and erected pre-fab hospitals all over Oman. Another large corporation had "something to do with" building the country's airports and another company helps "run" them.

Dr. Zawawi's brother, Qais Zawawi, the foreign minister, is listed as "general manager" of Waleed Associates in World Trade Reports.

The company offers "construction services" and deals in machinery, household appliances, mining machinery, communications equipment, outboard and inboard motors and scientific instruments.

Zawawi's family is one of the wealthiest in Oman. "You can drive from one end of Muscat [the capital] to the other," says a source who knows Oman well, "and it's Zawawi this and Zawawi that -- just read the signs, Zawawi . . . Zawawi . . . Zawawi."

It was Zawawi, says the source, who arranged for former president Gerald Ford and Scowcroft to visit Oman by private jet last year on undisclosed "business."

Zawawi himself visits Washington "quite often . . . at least a half-dozen times a year," the source says.

His interests are represented here by Helen Burbury, who is listed on "ISI" corporation papers filed in the as secretary-treasurer and a director. "

Burbury, from New Zealand, is one of a corps of English-speaking, United Kingdom secretaries employed by Zawawi in capitals all over the world to oversee his investments.

He maintains a home in Northern California on the Oregon border "because he likes trees," says one source. "If you were raised with nothing but sand, you'd like trees, too."

He has another house in Orlando, Fla., the same source says, "because his kids like Disney World."

Scowcroft and Brennan and Smith declined repeatedly last week to take telephone calls. Watson, now president of Dallas Baptist College, was "away" and could not be contacted. Gulley, now listed as president of ISI, was traveling in the Middle East, and a secretary said he could not be reached.

A former White House associate of Scowcroft, Brennan and Gulley's during the Nixon administration says that it was no secret among their friends that the three of them "had set up a company to do business in the Middle East and that Marvin Watson -- at one point -- was running it out of Los Angeles."

The only person ever connected with the venture who is willing to talk about it at all is Lawrence Traut of Cleveland, Ohio, who describes himself as "the only nonmilitary" American and a retired drug company manufacturer.

At one point, he was listed as the company's president.

He doesn't know, he says, how the group got involved with Zawawi. "But we had him checked out with all the major agencies -- state and CIA -- he's clean."

Traut says that Zawawi "met early in the Carter administration with [hamilton] Jordan" and the meeting apparently was not a huge success. ISI was formed in Panama about that time.

"We [the United States] were invited [into Oman] before," Traut says. "Now we are going to have to buy our way in."

One American businessman just returned from Oman says the "sultan is anxious for America to come in . . . they're unhappy with the British."

Even America's limited presence at the moment is creating new business opportunities. Former secretary of the Navy Bill Middendorf said last week that he had called the Navy brass at the Pentagon in behalf of a Lebanese catering firm, Arbela, which transports food to oil drilling rigs in the North Sea.