Venus Williams and Vera Zvonareva registered second-round victories at the Advanta Championships in Philadelphia on Thursday to remain in the chase for places in next week's lucrative end-of-season tournament.

Fifth seed Williams of the U.S., who is battling her sister Serena, Zvonareva and Jennifer Capriati for the two remaining berths in the $3 million WTA Tour Championships, moved into the quarter-finals by defeating Ukraine's Yuliana Fedak 6-4, 2-6, 7-6.

Earlier, sixth-seeded Russian Zvonareva, who must win in Philadelphia to clinch a spot in the elite eight-player field in Los Angeles next week, also needed three sets to oust Nathalie Dechy of France 2-6, 6-3, 6-4.

Top seed and defending champion Amelie Mauresmo of France, looking for her fifth title of the season and second in as many weeks, swept past Czech Republic's Iveta Benesova 6-2, 6-2.

"I feel comfortable playing here and hopefully it will keep going well," said Mauresmo. "I needed a couple of games to get into the rhythm.

FIRST SERVE

"I was able to count on my first serve today and that helped a lot. I was also able to close it out pretty quickly, which gives me a lot of confidence.

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"I really want the (world) number one spot back. I feel very proud about it, knowing I was the first Frenchwoman to do that. I want to do everything I can to get it back."

Second seed Anastasia Myskina, losing finalist last year, downed Paraguay's Rossana Neffa-De Los Rios 6-4, 7-6.

"It was a pretty good match for me," Russian Myskina said. "She was playing really well. I didn't expect so much from her since she's been out with injuries."

In other second-round action, eighth seed Alicia Molik of Australia put out Serbia and Montenegro's Jelena Jankovic 7-5, 6-3 and seventh seed Nadia Petrova of Russia tamed American Amy Frazier 6-4, 6-3 as the top eight seeds marched into the quarter-finals.