Federer, the 2009 champion, needed only one hour 36 minutes to see off Germany's lucky loser Oscar Otte.

The Swiss third seed, playing in the tournament for the first time since 2015, beat the world 144 6-4 6-3 6-4.

Spain's defending champion Nadal eased to a 6-1 6-2 6-4 win over German world number 114 Yannick Maden.

It was difficult - Federer

Otte held his serve in his opening four services games but was broken in his fifth as Federer took the opening set.

The 37-year-old then took control to move two sets ahead and a break in the ninth game of the third set gave him the opportunity to clinch an assured victory on his serve.

Otte had lost in the third qualifying round but took his place in the main draw as a 'lucky loser' because of withdrawals.

"The Grand Slams are incredible. You can meet a player who qualified who you have not heard of before," said Federer, who saved four break points.

"It was difficult. He really played a great match. Happily for me, he helped me with some mistakes at the end of the sets."

Federer next faces Norway's Casper Ruud, who knocked out Italian 29th seed Matteo Berrettini 6-4 7-5 6-3.

Nadal won the first five games of the match on his way to taking the opening set and broke 29-year-old Maden's serve in the opening service game of the second.

Playing in the second round of a Grand Slam for the first time, Maden broke Nadal's serve twice in the third set, but struggled to hold on to his own as the second seed moved into the last 32.

Maden is the second German qualifier that Nadal has beaten at this year's French Open after his first-round win over Yannick Hanfmann on Monday.

Nadal, who will face Belgium's David Goffin in round three, said: "It was a good match for the first two sets.

"Then in the third, being honest, I lost a little bit of concentration and intensity and then the match became difficult. The positive thing is every time I made a mistake, then I had the break again."

Tsitsipas, Nishikori & Wawrinka advance, but Cilic out

Sixth seed Stefanos Tsitsipas of Greece beat Bolivia's Hugo Dellien 4-6 6-0 6-3 7-5, while Japan's Kei Nishikori, seeded seventh, overcame France's Jo-Wilfried Tsonga 4-6 6-4 6-4 6-4.

Swiss former champion Stan Wawrinka defeated Chile's Cristian Garin 6-1 6-4 6-0 to set up a third-round meeting with Bulgaria's Grigor Dimitrov, who beat former US Open winner and 11th seed Marin Cilic 6-7 (3-7) 6-4 4-6 7-6 (7-2) 6-2.

France's Corentin Moutet, the world number 110, shocked Argentina's 19th seed Guido Pella 6-3 6-1 2-6 7-5.

Benoit Paire claimed a thrilling five-set win over fellow Frenchman Pierre-Hugues Herbert.

Paire won the opening two sets and was a break up in the third, before eventually winning 6-2 6-2 5-7 6-7 (6-8) 11-9 in an epic match that took four hours 33 minutes.