Kim Clijsters and Venus Williams both went through to the third round of the US Open with straight sets victories.

Reigning champion Clijsters insisted her game was still a work in progress despite easing to a 6-2 6-1 victory over Australian Sally Peers.

Clijsters has lost just eight games so far at Flushing Meadows but admitted there was plenty of room for improvement after dropping her serve twice against qualifier Peers.

The 27-year-old Belgian, who won the title 12 months ago in only her 14th match and third tournament since coming out of retirement, also managed to get just 51% of her first serves in and committed 21 unforced errors.

“I just had to find my footing again a little bit,” said Clijsters, who is seeded second this year behind Denmark’s Caroline Wozniacki, the player she beat in last year’s final.

“I felt as the match went on I got to read her game a bit better and moved a bit better, but I still have a little further to go before I play my best tennis.”

Elsewhere, third seed Venus Williams was pushed all the way by aggressive Canadian qualifier Rebecca Marino in the second round of the US Open.

Williams, a two-time champion at Flushing Meadows, needed a tie-break to win an opening set containing no breaks of serve.

The American finally broke in the fourth game of the second set to take a 3-1 lead before going on to post a 7-6 6-3 victory.

Williams will meet another qualifier in the third round, Luxembourg’s world number 185 Mandy Minella, who beat 32nd seed Tsvetana Pironkova for the loss of just four games.

Former world number one Ana Ivanovic booked her place in the third round of a grand slam for the first time this year following an upset win over China’s Zheng Jie.

The Serb brushed aside her 21st-seeded opponent 6-3 6-0 in less than an hour as she showed signs of the form that helped her reach the top of the women’s game.

Ivanovic, currently ranked 40 in the world, hit 22 winners in an unexpectedly dominant display in stiflingly hot conditions at Flushing Meadows.

Ivanovic next faces Virginie Razzano, who stunned 13th seed and former Wimbledon finalist Marion Bartoli.

“I remember a couple of years ago when I was here and I was saying, even though I’m number one I don’t feel I’m playing as number one,” Ivanovic said.

“But now I feel like I’m playing like a top-10 player. I have confidence that I can beat these players. That’s huge for me.

French Open champion Francesca Schiavone enjoyed a comfortable passage into the third round with a 6-2 6-1 victory over Italian qualifier Maria Elena Camerin.

However, 24th seed Daniela Hantuchova was given a stern test by Wimbledon ladies doubles champion Vania King, who took the opening set 7-5 on Louis Armstrong Stadium.

However, the Slovakian fought back to take the next two sets 6-3 6-4 to set up a clash with 12th seed Elena Dementieva, who enjoyed a 6-3 6-4 victory over Sybille Bammer.

Anastasia Pavlyuchenkova, seeded 20th, also advanced to the third round with a 6-2 6-4 win over India’s Sania Mirza.