Roddick, who won the tournament three consecutive years from 2003-2005, swept past Radek Stepanek 6-4, 6-4 in second-round play of the grass-court tournament.
Ljubicic also had little trouble in his 6-3, 6-4 straight-set win over Danai Udomchoke.
Top-seed Rafael Nadal and defending champion Lleyton Hewitt open their tournament in the second round Wednesday. The tournament's top eight seeds received first-round byes.
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