Federer beat 268th-ranked Ilija Bozoljac 6-4 7-5 6-2 while Wawrinka, fresh from winning his maiden grand slam title at the Australian Open, eased past Dusan Lajovic 6-4 4-6 6-1 7-6(7).
France got off to a flier against Australia with Jo-Wilfried Tsonga beating gutsy veteran Lleyton Hewitt 6-3 6-2 7-6(2) after Richard Gasquet outclassed Nick Kyrgios 7-6(3) 6-2 6-2.
The Czechs, who retained the Davis Cup in November, were losing 1-0 to the Netherlands in Ostrava, with Radek Stepanek going down in five sets to Robin Haase before Tomas Berdych plays Igor Sijsling later on Friday.
(Reporting by Toby Davis; Editing by Ken Ferris)