Federer needed only 96 minutes to beat Germany's Oscar Otte 6-4, 6-3, 6-4.

Next up for Federer is Norway's Casper Ruud, who caused one of the few upsets today when he knocked out Italian 29th seed Matteo Berrettini.

The 11-time champion Nadal meanwhile was a predictably easy winner against another German, world number 114 Yannick Maden, 6-1, 6-2, 6-4.

Maden, a 29-year-old qualifier playing in the second round of a Gran Slam for the first time, broke Nadal twice in the third set but could not hold on to his own.

Nadal is now due to play either Belgium's David Goffin or Serbia's Miomir Kecmanović next.

One player who could upset the established top order is Greek world number six Stefanos Tsitsipas, who fought from a set down to beat Bolivia's Hugo Dellien 4-6, 6-0, 6-3, 7-5.

There was home disappointment in Paris as Jo-Wilfried Tsonga lost 4-6 6-4 6-4 6-4 to Japan's world number seven Kei Nishikori.

The French fans were delighted, however, by arguably the biggest upset of the day - world number 110 Corentin Moutet beat 19th seed Guido Pella, from Argentina, 6-3, 6-1, 2-6, 7-5.

It was similarly simple for the big hitters in the women's game, as world number two Karolina Plíšková remains in the hunt for her first Grand Slam title.

The Czech crushed Slovakia's Kristina Kučová 6-2, 6-2 in under an hour, hitting 25 winners and six aces.

The Untied States seventh seed and 2018 runner-up Sloane Stephens, from the United States, is also safely through to round three, beating Spanish world number 75 Sara Sorribes Tormo 6-1, 7-6.

Spain's 2016 French Open champion Garbiñe Muguruza is also into the next round, seeing off Sweden's Johanna Larsson 6-4, 6-1.

Muguruza is set to play ninth seed Elina Svitolina next after the Ukrainian received a walkover when compatriot Kateryna Kozlova pulled out with an injury.