Flushing Meadows, NY -- (Sports Network) - Two-time champion Venus Williams was an easy third-round winner Saturday at the U.S. Open.

A seventh-seeded Venus swatted 27th-seeded Alona Bondarenko 6-2, 6-1 in a brisk 56-minute affair at Ashe Stadium. The former world No. 1 Venus ripped nine aces and did not allow even one break-point chance for her overmatched Ukrainian counterpart, who had her serve broken on four occasions en route to defeat.

The reigning two-time Wimbledon champion Venus was the back-to-back U.S. Open champ in 2000 and 2001 and runner-up here in 1997 and 2002. The powerful American is a seven-time major titlist, including a whopping five Wimbledon championships.

Venus could meet her fellow former No. 1 sister Serena in the quarterfinals here next week. The superstar siblings are the only former U.S. Open champions remaining in the women's draw.

The 28-year-old Venus could have her hands full with ninth-seeded Pole Agnieszka Radwanska in a fourth-rounder here on Monday. The talented Radwanska rolled past 18th-seeded Slovakian Dominika Cibulkova 6-0, 6-3 in 1 hour, 18 minutes on Day 6 at the USTA Billie Jean King National Tennis Center.

Another former world No. 1 advanced on Saturday, as 32nd-seeded Amelie Mauresmo ended the Cinderella run of fellow Frenchwoman Julie Coin in 6-4, 6-4 fashion. Earlier this week, the 188th-ranked Coin posted one of the greatest upsets in tennis history by shocking top-ranked Ana Ivanovic in the second round.

Mauresmo is a two-time major titlist who has been plagued by injuries over the past two seasons. She was ranked No. 1 during the 2006 campaign.