Women’s number one Angelique Kerber defeated Czech Republic’s Kristyna Pliskova (6-0, 6-4) and now faces Coco Vandeweghe in the next round.
Kerber earlier defeated Canada’s Eugenie Bouchard in three. (6-4, 3-6, 7-5).
Men’s number one Andy Murray also had a straight-sets victory over the USA’s Sam Querry (6-4, 6-2, 6-4).
Murray, who’s aiming to win the title after finishing runner-up five times, will now face Germany’s Mischa Zverev.
After Novak Djokovic’s surprise second-round exit, Murray is the clear favourite to win the championship.
But he says he’s trying to focus on his own game rather than the eventual outcome.
Former world number one Roger Federer had another successful night on the court, beating Czech Tomas Berdych in straight sets (6-2, 6-4, 6-4).
Federer will next face Japan’s Kei Nishikori.

Svetlana Kuznetsova was also a winner in a match that lasted three hours and 36 minutes.
The Russian eighth seed defeated Serbia’s Jelana Jankovic in three sets (6-4, 5-7, 9-7), saying she faced tough competition.

Anastasija Sevastova from Latvia, however, couldn't cope with very strong competitor, Spaniard Garbiñe Muguruza who won two sets 6-4 6-2. Nevertheless, Anastasija is happy with the performance in Australia this year
