Nadal beat Karol Beck of Slovakia 6-1, 6-2, and Federer defeated Andreas Seppi of Italy 6-3, 6-3.
"I am happy because it was an important win,'' said Nadal, who was broken once but took advantage of 27 unforced errors from Beck. "Yesterday, I played good and today also I played good.''
"I can't say if I am close to my best,'' added Nadal, who won both the French Open and Wimbledon in 2008. "You can never tell whether you are at your best. You can never tell about your level.''
The top-ranked Spaniard will next play fifth-seeded Gael Monfils of France on Thursday.
Federer was also broken once, but the 13-time Grand Slam champion from Switzerland still managed to beat Seppi, who committed 31 unforced errors - two more than Federer, who will play Philipp Kohlschreiber of Germany.
"It was a little difficult out there because he is a tough, steady player,'' Federer said. "There were no free points, but I am happy to have a good outing.''
Andy Roddick edged Arnaud Clement of France 6-3, 7-5 and will now play Victor Hanescu of Romania.
Andy Murray, who lost to Federer in last year's U.S. Open final, defeated Philipp Petzschner of Germany 6-2, 6-4 and will take on Sergiy Stakhovsky of Ukraine. The fourth-ranked Briton broke Petzschner twice in the first set and once in the second.
"I started really well, created chances on his serve,'' Murray said. "He was unpredictable at the start, but I managed to get ahead and keep my momentum and that always helps.''
Unlike Nadal and Federer, Murray was not broken in the match.
"My first serve percentage was good,'' Murray said. "I know he uses a lot of backhand slice shots, so I was able to keep my shots hard and flat. I think it was a good match for this stage of the tournament.''
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