Chinese player Li Na stormed into the last 16 in the women's draw of the US Open, beating Laura Robson 6-2, 6-2 while Novak Djokovic booked his spot in the last 32, beating Germany's Benjamin Becker 7-6, 6-2, 6-2.
Andy Murray too moved through to the next round but only after facing some resistance from Argentine Leonardo Mayer, winning 7-5, 6-1, 3-6, 6-1.
Tomas Berdych of the Czech Republic also went safely into the next round, dispatching USA's Denis Kudla 7-6, 7-6, 6-3.
In the women's draw, American Sloane Stephens beat compatriot Jamie Hampton 6-1, 6-3 while Jelena Jankovic beat Japanese Kurumi Nara 6-4, 7-6.
China's Jie Zheng, who knocked out Venus Williams, lost to Carla Suarez Navarro of Spain.