Roddick beats Stepanek at Queen's Club
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The American has lost just one match in his past four appearances at the Wimbledon warmup event, winning three straight titles before losing to James Blake in the 2006 semifinals.
"That felt really good out there today," Roddick said. "Looking at the draw, there's probably him and Ivo Karlovic as the two guys you don't want to see in the first round."
Roddick served 12 aces and converted his only break-point opportunity in the opening set to lead 4-3 after a backhand error by Stepanek.
In the second set, Roddick again set up break point at 3-3 with a forehand pass, but slipped when Stepanek wrong-footed him with a volley at the net. Roddick eventually broke at 4-4 when Stepanek made two straight backhand errors.
Stepanek twice wanted to challenge a point, but the electronic line-calling system being used on grass for the first time -- Hawk-Eye -- was unavailable because of a power problem.
Roddick had no sympathy for his opponent's frustration.
"It's a machine," he said. "Machines break, right? If it's working, you use it. If it's not, tough stuff."
Roddick, a former U.S. Open champion now ranked fifth in the world, won the Queen's Club tournament from 2003 to 2005. He was runner-up to Roger Federer at Wimbledon in 2004 and 2005.
In the first round, Karlovic beat ninth-seeded Mardy Fish of the United States 6-3, 6-4 behind 19 aces.
Croatian wild card Marin Cilic defeated Tim Henman of Britain 7-6 (5), 2-6, 6-4 for his first ATP Tour victory since July 2006. Henman has won only once on the tour this year.
Also, Sebastien Grosjean of France beat Michael Berrer of Germany 6-4, 6-2, and Jo-Wilfried Tsonga of France beat Kristian Pless of Denmark 7-6 (2), 6-0.
Top seed Rafael Nadal, who like Roddick had a bye to the second round, begins his grasscourt campaign on Wednesday allowing him an extra day to rest following his French Open victory over Federer on Sunday.
The Associated Press and Reuters contributed to this report.