Australia, after winning the toss, declared their first innings on an overnight score of 413 for nine against Derbyshire before play resumed on the second day of a three-day tour match at Derby on Friday.
Openers David Warner and Shaun Marsh both retired out on 101, with all-rounders Shane Watson (61) and Mitchell Marsh (53) each making a fifty.
Teenage paceman Will Davis took three for 63 on his first-class debut, the 19-year-old`s haul including the prized wicket of Australia captain Michael Clarke for just 16.
Pat Cummins, in his first match at this level for nearly two years because of injury problems, was 21 not out at stumps on Thursday, with Fawad Ahmed unbeaten on four.
Australia levelled the five-match Ashes series against England at 1-1 with a dominant 405-run win in the second Test at Lord`s on Sunday.
Australia were playing both their wicket-keepers in this match after Peter Nevill impressed on his debut at Lord`s -- a match first-choice gloveman Brad Haddin missed for "family reasons".
However, it was Nevill who was behind the stumps when Derbyshire`s innings started, with Haddin in the outfield.
That suggested Nevill, Haddin`s deputy at New South Wales, would keep wicket in the third Test at Edgbaston in Birmingham which starts on Wednesday.