NEW YORK — Now comes a challenge for Venus Williams and Serena Williams at the U.S. Open: a match against each other.

Except unlike so many of their all-in-the-family faceoffs at Grand Slam tournaments, including at Wimbledon in July, this Williams vs. Williams showdown will not decide the championship. Instead, this one will come in the quarterfinals.

Both advanced through the fourth round quite easily today. The No. 7-seeded Venus dismissed No. 9 Agnieszka Radwanska of Poland 6-1, 6-3, before No. 4 Serena dispatched wild-card entrant Severine Bremond of France 6-2, 6-2 at night.

"Even the semis would have been better than the quarterfinals, but at least one of us will make it to the semis," Serena told the crowd during an on-court interview. "I've got probably the toughest match of the tournament coming up next, so I've got to be ready."

Some sisters make plans to go shopping together, say, or to catch a movie. These siblings keep meeting up on tennis courts at the sport's highest levels.

"The best part is that we're still here," Venus said, "going stronger than ever, in my opinion."

Their matchup Wednesday will be a tiebreaker of sorts.

They've played 16 times as professionals, with each winning eight. That includes 10 meetings at major tournaments, with each winning five. The most recent was when Venus beat Serena for the title at the All England Club, the seventh all-Williams Grand Slam final.

"I would love to have a winning record," Venus said. "I have a chance."

Because of the luck of the pre-tournament draw, they were placed in the same portion of the bracket in New York — much to the disappointment of them, U.S. Open organizers and TV types. Even other players.

"For sure, it would have been better for the crowd if it was a final," Bremond said. "It would have been a very good final."

That certainly rings true: Venus has lost a total of 15 games through four matches at Flushing Meadows, while Serena has lost 14.

Of the eight women left in the tournament, only two have won a Grand Slam title: Serena leads all active players with eight, and Venus is right behind with seven.

They won every U.S. Open women's singles championship from 1999 to 2002, meeting in the finals the last two years in that span. Since then, though, Serena hasn't made it past the quarterfinals here, and Venus has only reached one semifinal.

Also advancing to the women's quarterfinals with victories Monday were No. 6 Dinara Safina, who defeated Anna-Lena Groenefeld 7-5, 6-0, and No. 16 Flavia Pennetta, who beat No. 32 Amelie Mauresmo 6-3, 6-0.

In men's action, No. 1 Rafael Nadal faced a tough challenge from 55th-ranked Sam Querrey, a 20-year-old Californian who never before had been to the fourth round at a major tournament.

Querrey hung in during extended baseline rallies, and even briefly led in the third set, before losing 6-2, 5-7, 7-6 (2), 6-3.

Nadal owns four titles from the French Open and one from Wimbledon, but he's never been as far as the U.S. Open semifinals. He'll try to take care of that gap on his resume when he meets another unseeded American, Mardy Fish, in the quarterfinals.

Also advancing: No. 17 Juan Martin del Potro of Argentina, who ended the run of Kei Nishikori, the first Japanese man to reach the U.S. Open's fourth round in the 40-year Open era. Del Potro won the contest between teenagers 6-3, 6-4, 6-3 for his 23rd consecutive victory.

Del Potro will face No. 6 Andy Murray or No. 10 Stanislas Wawrinka, who were playing Monday night's last match.

Fish beat a seeded player for the third consecutive match, serve-and-volleying his way past No. 32 Gael Monfils in straight sets Monday.

As for facing Nadal?

"I feel like a guy with my style of play is someone that he doesn't want to see," said Fish, who kept charging forward against Monfils and won the point of 45 of 69 trips to the net. "You've got to be able to finish points quickly. He's going to last longer than anybody. He wants to keep the points as long as possible and run the guys down, kind of body-blow after body-blow."

Nadal, who's won 42 of his past 43 matches, had to work hard to wear down the 6-foot-6 Querrey. When Nadal served for a two-set lead, Querrey broke him at love. When Nadal was trying to put the kid away, serving with a 4-2 edge in the fourth set, Querrey compiled seven break points.

"The match was crazy like that, no?" Nadal said.

He saved each of those seven break points, though, and that pretty much was that.

"He had to earn it," Querrey noted proudly. "I didn't just give it to him."