Leander Paes, a day after confirming to compete in the Olympics, got together with Stepanek to dispatch Israel's Andy Ram and Jonathan Elrich 6-2, 6-4, 7-6 in another second round match.
The fourth seeds next take on either Martin Emmrich and Michael Kohlmann from Germany or the Croatian-Brazilian combine of Ivan Dodig and Marcelo Melo.
Paes-Stepanek put 74 percent of their first serves and converted four of their 12 break points. Their opponents secured the lone break point opportunity they got and had the first serve percentage of 59.
Rohan Bopanna and China's Zheng Jie play their second round mixed doubles match later in the day.