MELBOURNE, Australia (AP) -- Venus Williams had to shake off some rust. Andre Agassi kept up his winning form from a warmup tournament.
Both advanced Monday to the second round of the Australian Open, where Agassi seeks his third title in four years and Williams tries to prevent a ''Serena Slam'' by her younger sister.
After falling behind 0-3 because of some wildness, Williams used a stronger serve to carry her through 6-4, 6-2 over 45th-ranked Svetlana Kuznetsova. She and the 17-year-old Russian were nearly even in errors.
''I'm just a little rusty,'' Williams said. ''I didn't expect to be 100 percent in this match, but in the next one I expect to be at least 150.''
Agassi overcame Brian Vahaly 7-5, 6-3, 6-3. He broke serve eight times against Vahaly, a former All-American at the University of Virginia.
Serena Williams starts action Tuesday against France's Emilie Loit. She is seeking a ''Serena Slam,'' in which she would hold all four of tennis' major titles at the same time.
Serena missed a chance for a true Grand Slam -- all four majors in one calendar year -- when she twisted her ankle just before last year's Australian Open. She went on to beat her sister in the finals at the French and U.S. Opens and Wimbledon.
Asked about beating Serena in this tournament, Venus said: ''I wouldn't exactly say that's my goal. My goal is to be my best. I guess if Serena wins a slam, then I'll be there congratulating her.''
In her last tournament before the Australian Open, Venus limped off with a lower leg strain while trailing Kim Clijsters 5-0 in the semifinals of the WTA Tour Championships in early November.
Serena, who lost to Clijsters in the November final, warmed up for the Open by playing in the Hopman Cup two weeks ago.
Paradorn Srichaphan, seeded 11th, opened play on center by beating Austrian Jurgen Melzer 7-5, 6-4, 1-6, 6-0.
''It's really special for me to play the first match on Monday, to open a Grand Slam, and I appreciate it,'' said Paradorn, who won two titles last year and beat Agassi at Wimbledon. Paradorn also beat No. 1 Lleyton Hewitt and No. 3 Marat Safin during the year.
Paradorn warmed up for the Open by winning another tournament earlier this month in India. He bowed Thai-style, with folded hands, to the crowd in Rod Laver Arena after forcing repeated errors by Melzer in the final set and watching a forehand volley by the Austrian sail long on the second match point.
In another Asian victory, South Korean Lee Hyung-taik, fresh from winning a warmup tournament in Sydney, beat Spain's David Ferrer 5-7, 6-2, 6-2, 6-3.
Anna Kournikova, unseeded after a year in which she lost in the first round at all four Grand Slams, defeated Slovakia's Henrieta Nagyova 6-1, 6-2.
French Open champion Albert Costa needed more than three hours for a 6-4, 6-1, 3-6, 7-6 (5) victory over German qualifier David Prinosil.
Costa, seeded eighth, reached the Top 10 for the first time last year despite skipping Wimbledon to concentrate on his new marriage. He wed longtime girlfriend Cristina Ventura five days after winning at Roland Garros.
No. 5 Carlos Moya defeated Belgian Dick Norman 7-5, 6-3, 6-4, No. 12 Sebastien Grosjean, a semifinalist in 2001, beat Fernando Meligeni 6-4, 6-2, 6-3, and No. 14 Guillermo Canas beat Vladimir Voltchkov of Belarus 6-3, 7-5, 6-3.
Wayne Ferreira, playing in his 50th Grand Slam tournament, ousted No. 26 Tommy Robredo 5-7, 6-0, 6-3, 6-4.
In other women's results, 2000 champion Lindsay Davenport, seeded ninth a year after knee surgery, beat wild-card entry Camille Pin 6-2, 6-1.
No. 5 Justine Henin-Hardenne, a Wimbledon semifinalist last year, defeated 17-year-old Swiss player Myriam Casanova 6-3, 6-4.
No. 7 Daniela Hantuchova defeated Fabiola Zuluaga 7-5, 6-7 (3), 6-4, No. 15 Alexandra Stevenson beat Elena Baltacha 6-1, 6-4, and No. 21 Ai Sugiyama beat Angelique Widjaja 6-3, 4-6, 6-2.
Like Serena Williams, Agassi has improved from last year just by starting the Australian Open.
He hurt his right wrist while losing last year's Kooyong Classic exhibition final against Pete Sampras two days before the Open's start, losing a chance to win the tournament three years in a row.
Nevertheless, he went right back to Kooyong this year. He won the Australian Open after winning at Kooyong in 2000 and 2001, and he won at Kooyong again Saturday, beating Grosjean 6-2, 6-3 in the final.
''This week I felt real good, a lot better a lot sooner than I was even hoping,'' said the 32-year-old American, oldest among the seeded men in the tournament.
Holding all four Grand Slam titles at once last was accomplished by Agassi's wife, Steffi Graf, who added the 1994 Australian title to her victories in the other majors in 1993.
Graf also is one of only three women with a true Grand Slam. She did that in 1988, following Maureen Connolly in 1953 and Margaret Court in 1970.
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