Andreev, the 2008 Gstaad runner-up, topped Jan Hernych of the Czech Republic 6-4 6-1. Chardy, the recent champion at Mercedes Cup in Stuttgart, Germany, toughed out a 6-3, 5-7, 6-3 win over Russian Mikhail Youzhny.
Chardy is 29-18 this season and was runner-up to France's Jo-Wilfried Tsonga at the SA Tennis Open in February.
Andreev lost to Romanian Victor Hanescu in last year's final.
In other matches Wednesday, German Andreas Beck outlasted Spaniard Guillermo Garcia-Lopez 7-6 (7-3), 1-6, 7-6 (7-3); and Romanian Victor Crivoi beat Russia's Teimuraz Gabashvili 6-4, 6-4.
Thursday's third-round matchups include top-seeded Stanislas Wawrinka of Switzerland, the 2005 runner-up, against Brazilian Thomaz Bellucci; Hanescu facing Florent Serra of France; Germany's Nicolas Kiefer, the sixth seed, against Spain's Ivan Navarro; and Brazil's Marcos Daniel meeting Frenchman Julien Benneteau.