Top-seeded Federer, set a record for consecutive victories on grass, as he got his 42nd straight win on the surface by beating Frenchman Richard Gasquet 6-3, 6-2, 6-2.
The world No. 1 Federer was leading Gasquet 6-3, 1-2 when their bout was halted because of rain here on Monday. The Swiss star won 11-of-13 games on Tuesday.
The second-seeded Nadal posted a 6-4, 7-6 (7-3), 6-4 decision against fellow lefthander, Britain's Alex Bogdanovic. Nadal, who could meet Agassi in the third round, will face American Robert Kendrick in the second.
Agassi, performing in his 14th and final Wimbledon, started slow against Serb Boris Pashanski before finding his footing en route to a 2-6, 6-2, 6-4, 6-3 victory.