Grosjean defeated Bjorn Phau of Germany, 4-6, 6-3, 7-5, Monday night, while Melzer beat Argentina's Mariano Puerta, 6-3, 6-3. They were the only seeds in singles action on the opening day of the tournament, where American Andy Roddick is the top seed.
Roddick will face a qualifier in his first-round match on Tuesday, while second-seeded Andre Agassi will play Michal Tabara of the Czech Republic.
In other matches Monday, Alex Calatrava of Spain kept 15-year-old wild card Donald Young of the United States winless. Young has an 0-5 record on the Tour after falling 6-1, 6-4. In a battle of Americans, Robby Ginepri defeated Mardy Fish, 6-1, 6-4.
Some information for this story provided by AP and AFP.