07/30/2012 09:51 EDT | Updated 09/29/2012 05:12 EDT

Wimbledon champs vs finalists at Olympics: Djokovic and Roddick, Serena Williams and Zvonareva

WIMBLEDON, England - In Andy Roddick's words, he and Novak Djokovic have been through it "a million" times — the pressure, the occasion and the formidable opponent. The Olympics, though, bring an unusual twist.

Roddick, a three-time Wimbledon finalist, and Djokovic, the 2011 champion at the All England Club, will play Tuesday in the second round of the Olympics. Both are wary of each other's weapons, and both embrace a sporting spirit that transcends individual achievement.

"Ninety-five per cent of the time, when a tennis player plays, it's for pretty selfish motives, and this week is not one of those," Roddick said Monday after defeating Martin Klizan of Slovakia, 7-5, 6-4. "So it is a different dynamic here."

Serena Williams beat Urszula Radwanska of Poland, 6-2, 6-3 in the second round on Court 1, just weeks after defeating Radwanska's sister, Agnieszka, in the Wimbledon final this month. On Wednesday, the five-time Wimbledon champion plays No. 13-seeded Vera Zvonareva, the Russian she beat in 2010 for the fourth of those titles.

"She's playing so well, moving well, doing everything great," Williams said. "It's not an easy tournament. You have to get out there. Playing someone so tough so soon, it's going to be a good challenge for me."

Top-seeded Roger Federer made a brief appearance on Centre Court, beating Julien Benneteau of France 6-2, 6-2 in less than an hour to reach the third round.

Second-seeded Djokovic, who lost to Federer in the semifinals at Wimbledon, would seem to have the edge over Roddick, whose world ranking has slipped to 22. The Serb was not complacent.

"Andy has one of the strongest serves in the world, ever, and it's his biggest weapon," Djokovic said. "The grass courts this year are very fast and it's a low bounce, so I think I will have to be on top of my game in order to win that match."

Even as he prepared for the contest, Djokovic relished the "special feeling" of being part of something larger, a team that represents his country.

"We all support each other, we all stay close to each other, and this is the important thing," he said. "We all try to enjoy every moment of it."

Roddick made similar remarks, saying it was an honour to be asked to play for the United States in the Olympics, and that he was happy that London was chosen for the event because it is a place he knows well. He said it was "my own fault" that he was facing Djokovic so soon in the tournament because he is unseeded.

"The guy has been the best player in the world over the last couple of years. It's going to be tough," Roddick said. "But the situation, we've both been through it a million times. I'm going to have to serve well and take some chances on returns."

Roddick's Olympic match, delayed a day by rain, was his first in eight years. He lost in the third round at the 2004 Games and skipped Beijing in 2008.

The Olympics have shaken up some of the tradition at Wimbledon, erecting purple backdrops and discarding the white-only rule for tennis garb. Roddick said he had taken some "wrong turns" around the grounds as he gets used to the different setup.

"We know that Wimbledon will be Wimbledon again next year," Federer said. "But right now, it's the Olympic Games. It is supposed to be different."

Also Monday, Venus Williams began her bid for a record fourth gold medal in Olympic tennis by beating Sara Errani of Italy, 6-3, 6-1.

It was an impressive showing from Williams, who is unseeded and drew a tough first-round foe. Errani has won four titles this year, was the runner-up at the French Open and is ranked a career-high No. 9.

But Williams was in fine form on the Wimbledon grass, where she has won five of her seven Grand Slam titles.

Venus Williams was diagnosed last year with an autoimmune disease that can cause fatigue, but she nonetheless began 2012 determined to make the Olympics for the fourth time. She won the gold medal in singles at the 2000 Games and teamed with Serena to take the gold in doubles in 2000 and 2008.

Top-seeded Victoria Azarenka of Belarus defeated Irina-Camelia Begu of Romania on Centre Court, 6-1, 3-6, 6-1.

Lleyton Hewitt of Australian and Nikolay Davydenko of Russia, both three-time Olympians, won their opening matches. No. 9-seeded Juan Monaco of Argentina, No. 13 Marin Cilic of Croatia, No. 16 Richard Gasquet of France and big-serving Milos Raonic of Canada also advanced.

In doubles, the Williams sisters began a bid for their third Olympic doubles gold medal by eliminating Sorana Cirstea and Simona Halep of Romania 6-3, 6-2. They won in 2000 and 2008. Federer and Stanislas Wawrinka, who won gold in 2008, defeated Kei Nishikori and Go Soeda of Japan, 6-7 (5), 6-4, 6-4.