NEW YORK -- The U.S. Open Tennis Championships begin Tuesday at the National Tennis Center in Flushing Meadow, N.Y. If you are wondering about an American male's chances of winning, keep your bets low and hold out for long odds.

The 16 men's seeds include four Swedes, four Americans, two Czechoslovakians, one West German, one Argentinean, one Australian, one Spaniard, one Frechman and one Ecuadorean.

The highest-seeded American, Jimmy Connors at No. 6, has not won a Grand Prix event since October 1984, and he will be 35 on Wednesday. John McEnroe, seeded eighth, could win but is not playing well and is in No. 1-seeded Ivan Lendl's quarter of the draw. On paper, McEnroe must defeat Lendl, Boris Becker and Stefan Edberg to win. Not likely.

The other two seeded Americans, No. 12 Tim Mayotte and No. 13 Brad Gilbert, face fifth-seeded Miloslav Mecir and Becker, respectively, so their chances are not promising, either. Some young nonseeded Americans do, however, have a chance to make names for themselves. Look for Jay Berger of Plantation, Fla., to possibly upset Gilbert in the second round, and Andre Agassi of Las Vegas to upset 11th-seeded Henri LeConte in the first round.

Scott Davis of Bardmoor, Fla., should scare Mecir in the round of 32. Rick Leach, the NCAA player of the year, or Paul Annacone (a two-time winner over McEnroe) may knock out Joakim Nystrom in the third round, and Dan Goldie of McLean, Va., should give Edberg a good match in the second round. The one other potential first-round upset involves Wimbledon champion Pat Cash. He could make an early exit at the hands of Peter Lundgren of Sweden.

Missing completely from the Open are Yannick Noah, who is ranked 10th in the world, and Kent Carlsson, who is ranked ninth. Noah has not played since Wimbledon and is in the midst of a sabbatical from the game.

Potential upsets aside, Lendl should repeat as the men's winner. Becker, McEnroe and Connors are in his half, but he is comfortable on these medium-speed cement courts. He should have no trouble at all reaching the quarterfinals. Second-seeded Edberg's path is more perilous and he may be pushed to five sets by his first-round opponent, Derrick Rostagno of Brentwood, Calif.

Two other Americans, David Pate and Kevin Curren, just missed being seeded because the U.S. Open committee adheres to a policy of seeding according to the Association of Tennis Professionals rankings. But it is long past due for separate world rankings for results on slow clay courts. Martin Jaite, a gifted clay courter, should not be seeded here on cement. Pate and Curren would have been the next two players with preferred slots in the draw.

The women's event is not likely to have as many upsets and the big news is: the Russians are coming. Top-seeded Steffi Graf will grab the headlines but pigtailed 16-year-old Natalia Zvereva will steal the hearts of the viewers.

Zvereva is the best player from the Soviet Union since Wimbledon finalist Olga Morozova and she reminds us of Andrea Jaeger. She won the junior Wimbledon title in a breeze and may face No. 3-seeded Chris Evert in the third round. She will not beat Evert but it will be fun to watch.

Pam Shriver, of Lutherville, Md., is playing the best tennis of her life, but is in Graf's quarter. If she beats Graf, she could go all the way. Evert, 32, is still dangerous. One gets the feeling that she just enjoys playing and, with less pressure to win, she can play much looser than before. She is seeking her seventh U.S. Open title.

Second-seeded Martina Navratilova feels uncomfortable in the No. 2 slot but in truth that is where she now belongs. The other U.S. seeds -- No. 7 Zina Garrison, No. 11 Lori McNeil and No. 15 Barbara Potter -- should reach the round of 16 comfortably. Bonnie Gadusek of Largo, Fla., unretired herself and may upset 16th-seeded Wendy Turnbull in the first round.

Other potential young American upsetters include Marianne Werdel of Bakersfield, Calif.; Ann Grossman of Grove City, Ohio, and two-time NCAA winner Patty Fendick of Sacramento, Calif.

Hovering in the background din of the Open is the hope that Americans do well this year. With losses to the West Germans in the Davis Cup and the Federation Cup and a poor showing at Wimbledon, this is our last chance this year. In the women's final Sept. 12, I am picking Graf to defeat Navratilova. In the men's final the next day, I am choosing Lendl over third-seeded Mats Wilander.