Now that a first-round opponent has been found for Jimmy Connors, a task that proved more difficult than expected, the U.S. Open Tennis Championships will begin Tuesday with both the men's and women's defending champions in action.

Connors, the winner of America's premier tennis tournament in 1974-76-78, is seeking to become the first man to successfully defend the title since Australian Neale Fraser did it in 1960. He will play his opener against Anand Amritraj of India -- the "second alternate" for the dubious honor -- in the featured match of Tuesday's evening session at the National Tennis Center.

Connor is seeded No. 2 in the men's singles draw of 128 to his archrival Bjorn Borg. Borg already has won the French Open and Wimbledon singles this year, each for the fourth time. Connors originally was drawn to play Austrian Davis Cup player Peter Feigl in the first round of the world's richest ($563,000 total prize money) tournament.

But Feigl, No. 47 in the current computerized world rankings of the Association of Tennis Professionals, cabled tournament officials from Europe over the weekend, saying he was withdrawing. His place was taken briefly by Sashi Menon of India, No. 151 on the computer and the first man accepted into the qualifying rounds.

But within two hours of his elevation to the main draw, Menon also pulled out. No reasons were given for either withdrawal, but a tournament official today winked and surmised that both Feigl and Menon had "suffered severely sprained expectations" when informed of the draw.

Dipping back into the pool of qualifying hopefuls, Referee Mike Blanchard came up with Amritraj, eldest of the three tennis-playing brothers from Madras and the No. 154 man on the most recent computer printout.

Amritraj assured Blanchard that he would show up to face Connors on the newly resurfaced hard court at the center of 19,000-seat Louis Armstrong Stadium, centerpiece of the handsome 25-court complex in Flushing Meadow Park, site of the 1939 and 1964 World's Fairs. The Open moved there last year after 54 years at the West Side Tennis Club in nearby Forest Hills.

Ironically, the winner of the Connors-Amritraj match will likely play another Amritraj brother in the second round; 25-year-old Vijay, who nearly beat Borg in a thrilling five-setter in the second round at Wimbledon this year.

Borg, 23, twice has been runner-up but never champion of the U.S. Open. For the second consecutive year, he enters the tournament with high hopes of grasping the third leg of the Grand Slam, a sweeo of the French. Wimbledon, U.S. and Australian titles that has been accomplished by only two men: California Don Budge in 1938 and Australian Rod Laver in 1962 and 1969.

Borg -- who reached the final last year, but developed a painful blister on his right thumb that hampered him in a straight sets loss to Connors -- is scheduled to play 1977 NCAA champion Matt Mitchell on Tuesday afternoon, the first of 10 day-night sessions.

Only one session is scheduled for each of the last three days. The men's and women's singles finals, each for a first prize of $39,000, will be played on Sunday, Sept. 9.The order will be decided by CBS-TV, which will televise live from 4-9 p.m. that day.

For the first time, women will share the opening-day program with men.

Chris Evert, who has won an astonishing 40 consecutive sets in U.S. Open competition since the 1975 final, is seeded No. 1 in her quest for a record fifth straight singles title.

Evert last year beat 16-year-old Pam Shriver in the final, equaling the record of four consecutive U.S. titles achieved previously by only two women: Norwegian-born Molla Bjurstedt Mallory in 1915-18 and Helen Jacobs in 1932-35.

Evert has won 50 of 51 sets in the last four Opens, dropping only one to Australian Evonne Goolagong Cawley -- the No. 5 seed this year -- in the 1975 final. Evert's victories on clay at Forest Hills in 1975-76-77 were expected, but her domination on the Open's new surface -- an asphalt-based hard court called Deco Turf II -- confirmed her greatness on all surfaces.

Evert plays the second stadium match Tuesday against Iris Reidel, 25, of West Germany, after the 11 a.m. curtain-raiser pairing Vitas Gerulaitis of nearby Kings Point, Long Island, against 1976 Australian Open champion Mark Edmondson.

Martina Navratilova, the expatriate Czech left-hander who has beated Evert in the Wimbledon final the past two years but was upset by Shriver in the semifinals here last year, is seeded No. 2 in the women's singles draw of 96. She has a first-round bye.

If the seedings were to hold true, the men's fourth-round pairings would be: Borg (seeded No. 1) vs. Adriano Panetta (16); Roscoe Tanner (5) vs. Tim Gullikson (14); Gerulaitis (4) vs. Jose Luis Clerc (10); Victor Pecci (8) vs. Wojtek Fibak (12); 1977 champion Guillermo Vilas (6) vs. Eddie Dibbs (9) ; John Mcenroe (3) vs. John Alexander (16); Harold Solomon (7) vs. Gene Mayer (13); and Connors (2) vs. Brian Gottfried (11).

The women's pairings at the same stage would be Evert (1) vs. Betty Stove (16), Goolagong (5) vs. Shriver (14), Virginia Wade (4) vs. Regina Marsikova (12), Wendy Turnbull (7) vs. Billie Jean King (9), Dianne Fromholtz (6) vs. Ann Kiyomura (15), Tracy Austin (3) vs. Kathy Jordan (11), Kerry Reid (8) vs. Sue Barker (13), and Narvatilova (2) vs. Greer Stevens (10).

For the first time in recent memory, all the top contenders in both men's and women's singles claim to be fit and ready, though Goolagong is just getting over a back injury and Shriver has been plagued all summer by tendinitis of the shoulder that has limited the effectiveness of her serve and overhead.

Fitness will play a large part in this Open, especially if the weather remains as hot and oppressively humid as it was today. For the first time since 1974, men's singles matches will be best-of-five-sets from the first round on. On physically demanding hard courts, this change -- favored almost unanimously by the top players -- will make the Open a championship test of endurance as well as all-court skill.