The American man is known as Ambassador Rambo. The Japanese man practices medieval swordsmanship _ the martial art of kendo, where duelists hit each other around the head with heavy bamboo poles.
They are the top officials fighting for their countries over access to each other's markets. And if they don't agree by 12:01 Thursday morning, 13 Japanese luxury cars will double in price. And that could be just the start of things.
They met Monday, and they will meet again today. So far, they are not close.
Among other things, U.S. Trade Representative Mickey Kantor, nicknamed Rambo for his tough style, wants the Japanese to use more American parts in their cars and to allow more American cars to be sold in Japan.
Japanese Trade Minister Ryutaro Hashimoto, the kendo master, says the unilateral threat by the United States violates global free trade rules.
Autos and auto parts account for about 60 percent of the $66-billion U.S. trade deficit with Japan last year.
Both sides are playing a high-stakes game. Both governments have domestic political problems and risk losing face if they make compromises.
If Japan refuses to make concessions, Washington has threatened huge tariffs on 13 luxury models built by Toyota, Honda, Nissan and Mazda.
This would double wholesale prices and sharply jack sticker prices. The Lexus LS480, for example, would rise in price from $55,000 to well over $80,000.
Japan says the United States has fallen behind Europe in winning market share because cars made by General Motors, Chrysler and Ford are too big. The Big Three also don't offer many models with steering wheels on the right side like Japan uses.
"Both countries are playing with fire," said Robert Hormats, a vice president at Goldman Sachs in New York. "You can't have a trade dispute of this magnitude between the two biggest financial powers in the world without an impact on other areas."
People looking at every nuance weren't sure what to make of one thing Monday. Kantor gave Hashimoto a shinai, a bamboo kendo sword. Noting that the Japanese minister was a great kendo tactician, Kantor said kendo fighters needed courage, honesty, integrity and patience _ all of which Hashimoto represented.
"I very much hope that we can carry on our conversations politely," replied Hashimoto, who had given Kantor a baseball bat during an earlier trade spat.
But if those discussions don't succeed _ and prospects are cloudy at best _ then analysts said U.S. policymakers should start making contingency plans to deal with the fallout from what threatens to become the biggest trade dispute since the 1930s.
Japan could impose its own punitive tariffs. High on the hit list are two of America's biggest sellers in the Japanese market _ food and aircraft.
The Japanese, however, might choose to retaliate in another way. Some think that Japan's recent rejection of President Clinton's call for a tougher economic embargo against Iran was just such a retaliation.
There also has been a rumor roiling U.S. financial markets that the Japanese might stop buying U.S. Treasury bonds. That would put upward pressure on American interest rates.
The economic fallout in Japan could be even worse. The Japanese economy already is teetering on the brink of another recession, with its exporters hurt by a yen that has gained 15 percent in value against the dollar since the first of this year.
"As is often the case when you have these kinds of fights, there are no winners," said Allen Sinai, chief economist at Lehman Brothers in New York.