Demsey birdied his first two holes to move to 10-under for the tournament, two shots off the lead.
Presnell birdied his first and third to get to the same score.
Martin Piller leads the Open at 12-under and tees off at 1.40pm.
New Zealand's hopes lie with Josh Geary and Grant Waite, who are both 11-under and have not yet teed off, as well as Steve Alker, who has played two holes and is 10-under.
It is another hot and sunny day at The Hills and organisers hope 10,000 fans will come to see the crowning of an Open champion.