Seeds Borna Coric and Benoit Paire were both beaten in the first round of the Lyon Open on Sunday.
Coric, a recent winner over world number one Andy Murray in Madrid, fell 6-4 5-7 6-4 to Georgia's Nikoloz Basilashvili, while Paire was beaten 6-7 (3/7) 7-6 (7/5) 6-4 by Australia's Jordan Thompson.
In the only first round match in the Geneva Open on Sunday, Andrey Kuznetsov fought back from behind to beat Thomaz Bellucci 3-6 6-4 6-1.
In the first round of the Strasbourg International, fourth seed Carla Suarez Navarro eased past Naomi Osaka of Japan 6-3 6-2.
Sixth seed Sam Stosur thrashed China's Ying-Ying Duan 6-0 6-1 in just 50 minutes, while there were also wins for Christina McHale, Amandine Hesse, Monica Puig and Ashleigh Barty.
Meanwhile on the first day of the Nuremberg Cup in Germany, there were wins for Kirsten Flipkens, Sorana Cirstea and Varvara Lepchenko.
