British trio Heather Watson, Harriet Dart and Katie Swan have all lost their Eastbourne first-round matches.
Watson, 27, who is British number two, was defeated by France's Alize Cornet 7-5 6-2.
While 22-year-old Dart lost 3-6 6-4 6-2 to 16th-seed Anett Kontaveit of Estonia and Swan, 20, fell 7-6 4-6 6-4 to China's Zhang Shuai.
British number one Johanna Konta starts at the Nature Valley International against Donna Vekic later on Sunday.