The nation's three major airline companies brought their heaviest hitters to town this week in a battle for a scarce but valuable commodity -- the right to fly from the United States to Japan.

One by one, American Airline's Chairman and President Robert L. Crandall, United's new chief executive Stephen Wolf and Texas Air Chairman Frank Lorenzo took their places on the witness stand in the Department of Transportation hearing room to argue why their airlines should be granted authority to fly from Seattle to Tokyo.

At stake is a foothold in the Pacific market, the fastest growing and one of the most lucrative markets for airline traffic.

"It's where all the growth is. It's growing by leaps and bounds. There's truly a lot of money out there," said Matthew V. Scocozza, DOT assistant secretary for policy and international affairs.

Between 1976 and 1986, the last year for which data is available, traffic between the United States and the Far East grew from 3.2 million passengers a year to 7.7 million passengers a year, with traffic between the United States and Japan growing from 2.4 million to 5 million passengers a year, according to Patrick V. Murphy, deputy assistant secretary of transportation.

Japan is now the second-largest market for overseas travel from the United States, surpassed only by the United Kingdom.

Although travel to Europe and domestic airline traffic are expected to continue to grow, those markets are relatively saturated compared with markets in the Pacific.

In addition to its potential for growth, the Pacific market is also dominated by business travel, which produces higher profits for airlines.

The recent imbalance between the yen and the dollar has also contributed to the attractiveness of the right to sell airline tickets to passengers who pay in yen.

United, the current holder of the route, won it in 1982 after a long battle. In 1985, United also acquired Pan American World Airways' extensive Pacific route network.

As a result, United acquired the right to serve Japan -- the principal gateway to other Pacific markets -- from Los Angeles and San Francisco. It also acquired crucial "beyond" rights -- permission to carry passengers beyond Tokyo to other destinations such as Hong Kong and Seoul.

The DOT set the reconsideration of United's right to the Seattle-Tokyo route when it approved the carrier's acquisition of Pan Am's Pacific division.

The prize in the DOT proceeding is the right to fly a single nonstop round-trip from the Seattle-Tacoma International Airport to Tokyo, with no right to carry passengers beyond that destination.

Even so, American and Continental are fighting vigorously to acquire the route, and United is fighting vigorously to keep it.

"Even though it may be a fairly limited route award, in order to do business long term in the Pacific it takes a long time, and you have to prove yourself, especially to foreign governments," said Paul Karos, an airline industry analyst with L.F. Rothschild Inc.

United, which made a major effort in those markets even during the takeover turmoil that surrounded its parent company, Allegis Inc. last year, now has 23 percent of the traffic between the United States and Japan.

Japan Air Lines is the leader in the market, with 30 percent of the traffic, followed by Northwest Airlines, a longtime provider of service to those markets that has about 28 percent of the traffic.

Winning the right for additional service from the United States to Japan -- which would require the consent of the Japanese government -- is difficult, said the airline executives.

As a result, the chance to provide service, however limited, has led to aggressive competition.

American argued that it would be a strong competitor against United and the other major carriers and that that competition would expand U.S. carriers' share of the market.

"We talk about the U.S. as a service economy -- one of the things we're going to have to export is service, and one of the services we are particularly good at is airline service," he said during the hearing Wednesday.

"In Europe and Asia and the Pacific, the U.S. ought to put the strongest team possible on the field," he said, noting that the United States has "in the Seattle-Tokyo case an opportunity to put a third strong player on the field."

American currently provides some nonstop service from Dallas to Tokyo.

Continental argued that, as a low-cost carrier, it would provide price competition against other carriers in the markets, despite assertions by American and United that Japan, which must approve fares, would resist lowering prices.

"We believe these markets are truly classic markets that are begging for the type of fare competition we can provide," said Lorenzo. "There's just a real perception that fares to this part of the world are very high."

United's argument is that it provides better service -- both in Seattle, where it has a hub, and in Tokyo -- and that retaining passengers on a U.S. carrier when they fly beyond Tokyo is in the best interest of U.S. trade.

Introducing new carriers to a market makes sense if it means expanding service, said Wolf.

In this case, however, "what you would do is reduce the capacity of a very vigorous U.S. carrier and replace it with one that wouldn't have the base in the Pacific and doesn't have the mass in Seattle."

In the long run, that might benefit JAL, United has argued.